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There are n lamps in a line. The lamps are numbered 1 to n from left to right. There are also n keys. When key number i is pressed, all lamps number x such that i|x change their state.For two integer numbers a and b, we say a|b if and only if there exists an integer c such that a × c = b.Amirali likes to play with the keys. He randomly pressed k keys and wants to know the final state of the lamps. Help him by writing a Pike piece of code to solve this task.

Input: ['2off off21 2'] Output:['on off ']

Shrek and the Donkey (as you can guess, they also live in the far away kingdom) decided to play a card game called YAGame. The rules are very simple: initially Shrek holds m cards and the Donkey holds n cards (the players do not see each other's cards), and one more card lies on the table face down so that both players cannot see it as well. Thus, at the beginning of the game there are overall m + n + 1 cards. Besides, the players know which cards the pack of cards consists of and their own cards (but they do not know which card lies on the table and which ones the other player has). The players move in turn and Shrek starts. During a move a player can: Try to guess which card is lying on the table. If he guesses correctly, the game ends and he wins. If his guess is wrong, the game also ends but this time the other player wins. Name any card from the pack. If the other player has such card, he must show it and put it aside (so that this card is no longer used in the game). If the other player doesn't have such card, he says about that. Recently Donkey started taking some yellow pills and winning over Shrek. Now Shrek wants to evaluate his chances to win if he too starts taking the pills.Help Shrek assuming the pills are good in quality and that both players using them start playing in the optimal manner.

Input: ['0 3'] Output:['0.25 0.75']

A very unusual citizen lives in a far away kingdom — Dwarf Gracula. However, his unusual name is not the weirdest thing (besides, everyone long ago got used to calling him simply Dwarf Greg). What is special about Dwarf Greg — he's been living for over 200 years; besides, he lives in a crypt on an abandoned cemetery and nobody has ever seen him out in daytime. Moreover, nobody has ever seen Greg buy himself any food. That's why nobody got particularly surprised when after the infernal dragon's tragic death cattle continued to disappear from fields. The people in the neighborhood were long sure that the harmless dragon was never responsible for disappearing cattle (considering that the dragon used to be sincere about his vegetarian views). But even that's not the worst part of the whole story.The worst part is that merely several minutes ago Dwarf Greg in some unintelligible way got inside your house and asked you to help him solve a problem. The point is that a short time ago Greg decided to order a new coffin (knowing his peculiar character, you are not surprised at all). But the problem is: a very long in both directions L-shaped corridor leads to Greg's crypt, and you can't drag just any coffin through that corridor. That's why he asked you to help. You've formalized the task on a plane like this: let the corridor's width before and after the turn be equal to a and b correspondingly (see the picture). The corridor turns directly at a right angle, the coffin is a rectangle whose length and width are equal to l and w (l ≥ w) correspondingly. Dwarf Greg has already determined the coffin's length (l), which is based on his height; your task is to determine the coffin's maximally possible width (w), at which it can be brought to the crypt. Besides, due to its large mass (pure marble!) the coffin is equipped with rotating wheels; therefore it is impossible to lift it off the ground, however, arbitrary moves and rotations of the coffin in the plane become possible. The coffin may be rotated arbitrarily just before you drag it into crypt and move through the corridor.Greg promised that if you help him, he will grant you immortality (I wonder how?). And if you don't, well... trust me, you don't want to know what happens if you don't help him...

Input: ['2 2 1'] Output:['1.0000000']

Vasilisa the Wise from a far away kingdom got a present from her friend Helga the Wise from a farther away kingdom. The present is a surprise box, yet Vasilisa the Wise doesn't know yet what the surprise actually is because she cannot open the box. She hopes that you can help her in that.The box's lock is constructed like that. The box itself is represented by an absolutely perfect black cube with the identical deepening on each face (those are some foreign nanotechnologies that the far away kingdom scientists haven't dreamt of). The box is accompanied by six gems whose form matches the deepenings in the box's faces. The box can only be opened after it is correctly decorated by the gems, that is, when each deepening contains exactly one gem. Two ways of decorating the box are considered the same if they can be obtained one from the other one by arbitrarily rotating the box (note that the box is represented by a perfect nanotechnological cube)Now Vasilisa the Wise wants to know by the given set of colors the following: in how many ways would she decorate the box in the worst case to open it? To answer this question it is useful to know that two gems of one color are indistinguishable from each other. Help Vasilisa to solve this challenging problem.

Input: ['YYYYYY'] Output:['1']

The Professor has lost his home robot yet again. After some thinking Professor understood that he had left the robot in the basement.The basement in Professor's house is represented by a rectangle n × m, split into 1 × 1 squares. Some squares are walls which are impassable; other squares are passable. You can get from any passable square to any other passable square moving through edge-adjacent passable squares. One passable square is the exit from the basement. The robot is placed exactly in one passable square. Also the robot may be placed in the exit square.Professor is scared of going to the dark basement looking for the robot at night. However, he has a basement plan and the robot's remote control. Using the remote, Professor can send signals to the robot to shift one square left, right, up or down. When the robot receives a signal, it moves in the required direction if the robot's neighboring square in the given direction is passable. Otherwise, the robot stays idle.Professor wrote a sequence of k commands on a piece of paper. He thinks that the sequence can lead the robot out of the basement, wherever it's initial position might be. Professor programmed another robot to press the required buttons on the remote according to the notes on the piece of paper. Professor was just about to run the program and go to bed, when he had an epiphany.Executing each command takes some energy and Professor doesn't want to get huge electricity bill at the end of the month. That's why he wants to find in the sequence he has written out the minimal possible prefix that would guarantee to lead the robot out to the exit after the prefix is fulfilled. And that's the problem Professor challenges you with at this late hour.

Input: ['5 5 7######...##...##E..######UULLDDR'] Output:['6']

One university has just found out about a sport programming contest called ACM ICPC v2.0. This contest doesn't differ much from the well-known ACM ICPC, for example, the participants are not allowed to take part in the finals more than two times. However, there is one notable difference: the teams in the contest should consist of exactly n participants.Having taken part in several ACM ICPC v2.0 finals and having not won any medals, the students and the university governors realized that it's high time they changed something about the preparation process. Specifically, as the first innovation it was decided to change the teams' formation process. Having spent considerable amount of time on studying the statistics of other universities' performance, they managed to receive some interesting information: the dependence between the probability of winning a medal and the number of team members that participated in the finals in the past. More formally, we know n + 1 real numbers p0 ≤ p1 ≤ ... ≤ pn, where pi is the probability of getting a medal on the finals if the team has i participants of previous finals, and other n - i participants arrived to the finals for the first time.Despite such useful data, the university governors are unable to determine such team forming tactics that would provide the maximum probability of winning a medal at ACM ICPC v2.0 finals on average (we are supposed to want to provide such result to the far future and we are also supposed to have an endless supply of students). And how about you, can you offer such optimal tactic? At the first stage the university governors want to know the value of maximum average probability.More formally, suppose that the university sends a team to the k-th world finals. The team has ak participants of previous finals (0 ≤ ak ≤ n). Since each person can participate in the finals no more than twice, the following condition must be true: . Your task is to choose sequence so that the limit Ψ exists and it's value is maximal:As is an infinite sequence, you should only print the maximum value of the Ψ limit.

Input: ['30.115590 0.384031 0.443128 0.562356'] Output:['0.4286122500']

Little Gennady was presented with a set of domino for his birthday. The set consists of 28 different dominoes of size 2 × 1. Both halves of each domino contain one digit from 0 to 6. 0-0 0-1 0-2 0-3 0-4 0-5 0-61-1 1-2 1-3 1-4 1-5 1-62-2 2-3 2-4 2-5 2-63-3 3-4 3-5 3-64-4 4-5 4-65-5 5-66-6The figure that consists of 28 dominoes is called magic, if it can be fully covered with 14 non-intersecting squares of size 2 × 2 so that each square contained four equal numbers. Every time Gennady assembles a magic figure, some magic properties of the set appear — he wins the next contest. Gennady noticed that he can't assemble a figure that has already been assembled, otherwise someone else wins the contest. Gennady chose a checked field of size n × m and put there rectangular chips of sizes 1 × 2 and 2 × 1. Each chip fully occupies exactly two neighboring squares of the field. Those chips do not overlap but they can touch each other. Overall the field has exactly 28 chips, equal to the number of dominoes in the set. Now Gennady wants to replace each chip with a domino so that a magic figure appeared as a result. Different chips should be replaced by different dominoes. Determine in what number of contests Gennady can win over at the given position of the chips. You are also required to find one of the possible ways of replacing chips with dominoes to win the next Codeforces round.

Input: ['8 8.aabbcc..defghi.kdefghijklmnopqj.lmnopq..rstuvw.xrstuvwyxzzAABBy'] Output:['10080.001122..001122.3344005533440055.225566..225566.6611334466113344']

Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Lucky number is super lucky if it's decimal representation contains equal amount of digits 4 and 7. For example, numbers 47, 7744, 474477 are super lucky and 4, 744, 467 are not.One day Petya came across a positive integer n. Help him to find the least super lucky number which is not less than n.

Input: ['4500'] Output:['4747']

Petya likes horse racing very much. Horses numbered from l to r take part in the races. Petya wants to evaluate the probability of victory; for some reason, to do that he needs to know the amount of nearly lucky horses' numbers. A nearly lucky number is an integer number that has at least two lucky digits the distance between which does not exceed k. Petya learned from some of his mates from Lviv that lucky digits are digits 4 and 7. The distance between the digits is the absolute difference between their positions in the number of a horse. For example, if k = 2, then numbers 412395497, 404, 4070400000070004007 are nearly lucky and numbers 4, 4123954997, 4007000040070004007 are not.Petya prepared t intervals [li, ri] and invented number k, common for all of them. Your task is to find how many nearly happy numbers there are in each of these segments. Since the answers can be quite large, output them modulo 1000000007 (109 + 7).

Input: ['1 21 100'] Output:['4']

Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than 4 and 7. For example, numbers 47, 744, 4 are lucky and 5, 17, 467 are not.Lucky number is super lucky if it's decimal representation contains equal amount of digits 4 and 7. For example, numbers 47, 7744, 474477 are super lucky and 4, 744, 467 are not.One day Petya came across a positive integer n. Help him to find the least super lucky number which is not less than n.

Input: ['4500'] Output:['4747']

One day Igor K. stopped programming and took up math. One late autumn evening he was sitting at a table reading a book and thinking about something. The following statement caught his attention: "Among any six people there are either three pairwise acquainted people or three pairwise unacquainted people"Igor just couldn't get why the required minimum is 6 people. "Well, that's the same for five people, too!" — he kept on repeating in his mind. — "Let's take, say, Max, Ilya, Vova — here, they all know each other! And now let's add Dima and Oleg to Vova — none of them is acquainted with each other! Now, that math is just rubbish!"Igor K. took 5 friends of his and wrote down who of them is friends with whom. Now he wants to check whether it is true for the five people that among them there are either three pairwise acquainted or three pairwise not acquainted people.

Input: ['41 32 31 45 3'] Output:['WIN']

Igor K. very much likes a multiplayer role playing game WineAge II. Who knows, perhaps, that might be the reason for his poor performance at the university. As any person who plays the game, he is interested in equipping his hero with as good weapon and outfit as possible. One day, as he was reading the game's forum yet again, he discovered a very interesting fact. As it turns out, each weapon in the game is characterised with k different numbers: a1, ..., ak. They are called hit indicators and according to the game developers' plan they are pairwise coprime. The damage that is inflicted during a hit depends not only on the weapon's characteristics, but also on the hero's strength parameter. Thus, if the hero's strength equals n, than the inflicted damage will be calculated as the number of numbers on the segment , that aren't divisible by any hit indicator ai.Recently, having fulfilled another quest, Igor K. found a new Lostborn sword. He wants to know how much damage he will inflict upon his enemies if he uses it.

Input: ['20 32 3 5'] Output:['6']

When Igor K. was a freshman, his professor strictly urged him, as well as all other freshmen, to solve programming Olympiads. One day a problem called "Flags" from a website called Timmy's Online Judge caught his attention. In the problem one had to find the number of three-colored flags that would satisfy the condition... actually, it doesn't matter. Igor K. quickly found the formula and got the so passionately desired Accepted.However, the professor wasn't very much impressed. He decided that the problem represented on Timmy's Online Judge was very dull and simple: it only had three possible colors of flag stripes and only two limitations. He suggested a complicated task to Igor K. and the fellow failed to solve it. Of course, we won't tell anybody that the professor couldn't solve it as well.And how about you? Can you solve the problem?The flags consist of one or several parallel stripes of similar width. The stripes can be one of the following colors: white, black, red or yellow. You should find the number of different flags with the number of stripes from L to R, if: a flag cannot have adjacent stripes of one color; a flag cannot have adjacent white and yellow stripes; a flag cannot have adjacent red and black stripes; a flag cannot have the combination of black, white and red stripes following one after another in this or reverse order; symmetrical flags (as, for example, a WB and a BW flag, where W and B stand for the white and black colors) are considered the same.

Input: ['3 4'] Output:['23']

After the Search Ultimate program that searched for strings in a text failed, Igor K. got to think: "Why on Earth does my program work so slowly?" As he double-checked his code, he said: "My code contains no errors, yet I know how we will improve Search Ultimate!" and took a large book from the shelves. The book read "Azembler. Principally New Approach".Having carefully thumbed through the book, Igor K. realised that, as it turns out, you can multiply the numbers dozens of times faster. "Search Ultimate will be faster than it has ever been!" — the fellow shouted happily and set to work.Let us now clarify what Igor's idea was. The thing is that the code that was generated by a compiler was far from perfect. Standard multiplying does work slower than with the trick the book mentioned.The Azembler language operates with 26 registers (eax, ebx, ..., ezx) and two commands: [x] — returns the value located in the address x. For example, [eax] returns the value that was located in the address, equal to the value in the register eax. lea x, y — assigns to the register x, indicated as the first operand, the second operand's address. Thus, for example, the "lea ebx, [eax]" command will write in the ebx register the content of the eax register: first the [eax] operation will be fulfilled, the result of it will be some value that lies in the address written in eax. But we do not need the value — the next operation will be lea, that will take the [eax] address, i.e., the value in the eax register, and will write it in ebx. On the first thought the second operation seems meaningless, but as it turns out, it is acceptable to write the operation as lea ecx, [eax + ebx],lea ecx, [k*eax]or evenlea ecx, [ebx + k*eax],where k = 1, 2, 4 or 8.As a result, the register ecx will be equal to the numbers eax + ebx, k*eax and ebx + k*eax correspondingly. However, such operation is fulfilled many times, dozens of times faster that the usual multiplying of numbers. And using several such operations, one can very quickly multiply some number by some other one. Of course, instead of eax, ebx and ecx you are allowed to use any registers.For example, let the eax register contain some number that we should multiply by 41. It takes us 2 lines:lea ebx, [eax + 4*eax] // now ebx = 5*eaxlea eax, [eax + 8*ebx] // now eax = eax + 8*ebx = 41*eaxIgor K. got interested in the following question: what is the minimum number of lea operations needed to multiply by the given number n and how to do it? Your task is to help him.Consider that at the initial moment of time eax contains a number that Igor K. was about to multiply by n, and the registers from ebx to ezx contain number 0. At the final moment of time the result can be located in any register.

Input: ['41'] Output:['2lea ebx, [eax + 4*eax]lea ecx, [eax + 8*ebx]']

Students love to celebrate their holidays. Especially if the holiday is the day of the end of exams!Despite the fact that Igor K., unlike his groupmates, failed to pass a programming test, he decided to invite them to go to a cafe so that each of them could drink a bottle of... fresh cow milk. Having entered the cafe, the m friends found n different kinds of milk on the menu, that's why they ordered n bottles — one bottle of each kind. We know that the volume of milk in each bottle equals w.When the bottles were brought in, they decided to pour all the milk evenly among the m cups, so that each got a cup. As a punishment for not passing the test Igor was appointed the person to pour the milk. He protested that he was afraid to mix something up and suggested to distribute the drink so that the milk from each bottle was in no more than two different cups. His friends agreed but they suddenly faced the following problem — and what is actually the way to do it?Help them and write the program that will help to distribute the milk among the cups and drink it as quickly as possible!Note that due to Igor K.'s perfectly accurate eye and unswerving hands, he can pour any fractional amount of milk from any bottle to any cup.

Input: ['2 500 3'] Output:['YES1 333.3333332 333.3333332 166.666667 1 166.666667']

Little walrus Fangy loves math very much. That's why when he is bored he plays with a number performing some operations.Fangy takes some positive integer x and wants to get a number one from it. While x is not equal to 1, Fangy repeats the following action: if x is odd, then he adds 1 to it, otherwise he divides x by 2. Fangy knows that for any positive integer number the process ends in finite time.How many actions should Fangy perform to get a number one from number x?

Input: ['1'] Output:['0']

There are n walruses sitting in a circle. All of them are numbered in the clockwise order: the walrus number 2 sits to the left of the walrus number 1, the walrus number 3 sits to the left of the walrus number 2, ..., the walrus number 1 sits to the left of the walrus number n.The presenter has m chips. The presenter stands in the middle of the circle and starts giving the chips to the walruses starting from walrus number 1 and moving clockwise. The walrus number i gets i chips. If the presenter can't give the current walrus the required number of chips, then the presenter takes the remaining chips and the process ends. Determine by the given n and m how many chips the presenter will get in the end.

Input: ['4 11'] Output:['0']

Yesterday was a fair in a supermarket's grocery section. There were n jars with spices on the fair. Before the event the jars were numbered from 1 to n from the left to the right. After the event the jars were moved and the grocer had to sort them by the increasing of the numbers.The grocer has a special machine at his disposal. The machine can take any 5 or less jars and rearrange them in the way the grocer wants. Note that the jars do not have to stand consecutively. For example, from the permutation 2, 6, 5, 4, 3, 1 one can get permutation 1, 2, 3, 4, 5, 6, if pick the jars on the positions 1, 2, 3, 5 and 6. Which minimum number of such operations is needed to arrange all the jars in the order of their numbers' increasing?

Input: ['63 5 6 1 2 4'] Output:['241 3 6 4 3 6 4 1 22 5 5 2 ']

There are n walruses standing in a queue in an airport. They are numbered starting from the queue's tail: the 1-st walrus stands at the end of the queue and the n-th walrus stands at the beginning of the queue. The i-th walrus has the age equal to ai.The i-th walrus becomes displeased if there's a younger walrus standing in front of him, that is, if exists such j (i < j), that ai > aj. The displeasure of the i-th walrus is equal to the number of walruses between him and the furthest walrus ahead of him, which is younger than the i-th one. That is, the further that young walrus stands from him, the stronger the displeasure is.The airport manager asked you to count for each of n walruses in the queue his displeasure.

Input: ['610 8 5 3 50 45'] Output:['2 1 0 -1 0 -1 ']

A newspaper is published in Walrusland. Its heading is s1, it consists of lowercase Latin letters. Fangy the little walrus wants to buy several such newspapers, cut out their headings, glue them one to another in order to get one big string. After that walrus erase several letters from this string in order to get a new word s2. It is considered that when Fangy erases some letter, there's no whitespace formed instead of the letter. That is, the string remains unbroken and it still only consists of lowercase Latin letters.For example, the heading is "abc". If we take two such headings and glue them one to the other one, we get "abcabc". If we erase the letters on positions 1 and 5, we get a word "bcac".Which least number of newspaper headings s1 will Fangy need to glue them, erase several letters and get word s2?

Input: ['abcxyz'] Output:['-1']

A group of university students wants to get to the top of a mountain to have a picnic there. For that they decided to use a cableway.A cableway is represented by some cablecars, hanged onto some cable stations by a cable. A cable is scrolled cyclically between the first and the last cable stations (the first of them is located at the bottom of the mountain and the last one is located at the top). As the cable moves, the cablecar attached to it move as well.The number of cablecars is divisible by three and they are painted three colors: red, green and blue, in such manner that after each red cablecar goes a green one, after each green cablecar goes a blue one and after each blue cablecar goes a red one. Each cablecar can transport no more than two people, the cablecars arrive with the periodicity of one minute (i. e. every minute) and it takes exactly 30 minutes for a cablecar to get to the top.All students are divided into three groups: r of them like to ascend only in the red cablecars, g of them prefer only the green ones and b of them prefer only the blue ones. A student never gets on a cablecar painted a color that he doesn't like,The first cablecar to arrive (at the moment of time 0) is painted red. Determine the least time it will take all students to ascend to the mountain top.

Input: ['1 3 2'] Output:['34']

The Fire Lord attacked the Frost Kingdom. He has already got to the Ice Fortress, where the Snow Queen dwells. He arranged his army on a segment n in length not far from the city walls. And only the frost magician Solomon can save the Frost Kingdom. The n-long segment is located at a distance equal exactly to 1 from the castle walls. It can be imaginarily divided into unit segments. On some of the unit segments fire demons are located — no more than one demon per position. Each demon is characterised by his strength - by some positive integer. We can regard the fire demons being idle.Initially Solomon is positioned on the fortress wall. He can perform the following actions several times in a row: "L" — Solomon shifts one unit to the left. This movement cannot be performed on the castle wall. "R" — Solomon shifts one unit to the left. This movement cannot be performed if there's no ice block to the right. "A" — If there's nothing to the right of Solomon, then Solomon creates an ice block that immediately freezes to the block that Solomon is currently standing on. If there already is an ice block, then Solomon destroys it. At that the ice blocks to the right of the destroyed one can remain but they are left unsupported. Those ice blocks fall down.Solomon spends exactly a second on each of these actions.As the result of Solomon's actions, ice blocks' segments fall down. When an ice block falls on a fire demon, the block evaporates and the demon's strength is reduced by 1. When the demons' strength is equal to 0, the fire demon vanishes. The picture below shows how it happens. The ice block that falls on the position with no demon, breaks into lots of tiny pieces and vanishes without hurting anybody. Help Solomon destroy all the Fire Lord's army in minimum time.

Input: ['31 0 1'] Output:['ARARARALLLA']

Let's consider the following game. We have a rectangular field n × m in size. Some squares of the field contain chips.Each chip has an arrow painted on it. Thus, each chip on the field points in one of the following directions: up, down, left or right.The player may choose a chip and make a move with it.The move is the following sequence of actions. The chosen chip is marked as the current one. After that the player checks whether there are more chips in the same row (or in the same column) with the current one that are pointed by the arrow on the current chip. If there is at least one chip then the closest of them is marked as the new current chip and the former current chip is removed from the field. After that the check is repeated. This process can be repeated several times. If a new chip is not found, then the current chip is removed from the field and the player's move ends.By the end of a move the player receives several points equal to the number of the deleted chips.By the given initial chip arrangement determine the maximum number of points that a player can receive during one move. Also determine the number of such moves.

Input: ['4 4DRLDU.UL.UURRDDL'] Output:['10 1']

It is nighttime and Joe the Elusive got into the country's main bank's safe. The safe has n cells positioned in a row, each of them contains some amount of diamonds. Let's make the problem more comfortable to work with and mark the cells with positive numbers from 1 to n from the left to the right.Unfortunately, Joe didn't switch the last security system off. On the plus side, he knows the way it works.Every minute the security system calculates the total amount of diamonds for each two adjacent cells (for the cells between whose numbers difference equals 1). As a result of this check we get an n - 1 sums. If at least one of the sums differs from the corresponding sum received during the previous check, then the security system is triggered.Joe can move the diamonds from one cell to another between the security system's checks. He manages to move them no more than m times between two checks. One of the three following operations is regarded as moving a diamond: moving a diamond from any cell to any other one, moving a diamond from any cell to Joe's pocket, moving a diamond from Joe's pocket to any cell. Initially Joe's pocket is empty, and it can carry an unlimited amount of diamonds. It is considered that before all Joe's actions the system performs at least one check.In the morning the bank employees will come, which is why Joe has to leave the bank before that moment. Joe has only k minutes left before morning, and on each of these k minutes he can perform no more than m operations. All that remains in Joe's pocket, is considered his loot.Calculate the largest amount of diamonds Joe can carry with him. Don't forget that the security system shouldn't be triggered (even after Joe leaves the bank) and Joe should leave before morning.

Input: ['2 3 12 3'] Output:['0']

Vasya studies music. He has learned lots of interesting stuff. For example, he knows that there are 12 notes: C, C#, D, D#, E, F, F#, G, G#, A, B, H. He also knows that the notes are repeated cyclically: after H goes C again, and before C stands H. We will consider the C note in the row's beginning and the C note after the H similar and we will identify them with each other. The distance between the notes along the musical scale is measured in tones: between two consecutive notes there's exactly one semitone, that is, 0.5 tone. The distance is taken from the lowest tone to the uppest one, that is, the distance between C and E is 4 semitones and between E and C is 8 semitonesVasya also knows what a chord is. A chord is an unordered set of no less than three notes. However, for now Vasya only works with triads, that is with the chords that consist of exactly three notes. He can already distinguish between two types of triads — major and minor.Let's define a major triad. Let the triad consist of notes X, Y and Z. If we can order the notes so as the distance along the musical scale between X and Y equals 4 semitones and the distance between Y and Z is 3 semitones, then the triad is major. The distance between X and Z, accordingly, equals 7 semitones.A minor triad is different in that the distance between X and Y should be 3 semitones and between Y and Z — 4 semitones.For example, the triad "C E G" is major: between C and E are 4 semitones, and between E and G are 3 semitones. And the triplet "C# B F" is minor, because if we order the notes as "B C# F", than between B and C# will be 3 semitones, and between C# and F — 4 semitones.Help Vasya classify the triad the teacher has given to him.

Input: ['C E G'] Output:['major']

Two best friends Serozha and Gena play a game.Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?

Input: ['3'] Output:['2']

Vasya the programmer lives in the middle of the Programming subway branch. He has two girlfriends: Dasha and Masha, who live at the different ends of the branch, each one is unaware of the other one's existence.When Vasya has some free time, he goes to one of his girlfriends. He descends into the subway at some time, waits the first train to come and rides on it to the end of the branch to the corresponding girl. However, the trains run with different frequencies: a train goes to Dasha's direction every a minutes, but a train goes to Masha's direction every b minutes. If two trains approach at the same time, Vasya goes toward the direction with the lower frequency of going trains, that is, to the girl, to whose directions the trains go less frequently (see the note to the third sample).We know that the trains begin to go simultaneously before Vasya appears. That is the train schedule is such that there exists a moment of time when the two trains arrive simultaneously.Help Vasya count to which girlfriend he will go more often.

Input: ['3 7'] Output:['Dasha']

A sequence a0, a1, ... is called a recurrent binary sequence, if each term ai (i = 0, 1, ...) is equal to 0 or 1 and there exist coefficients such that an = c1·an - 1 + c2·an - 2 + ... + ck·an - k (mod 2),  for all n ≥ k. Assume that not all of ci are zeros.Note that such a sequence can be uniquely recovered from any k-tuple {as, as + 1, ..., as + k - 1} and so it is periodic. Moreover, if a k-tuple contains only zeros, then the sequence contains only zeros, so this case is not very interesting. Otherwise the minimal period of the sequence is not greater than 2k - 1, as k-tuple determines next element, and there are 2k - 1 non-zero k-tuples. Let us call a sequence long if its minimal period is exactly 2k - 1. Your task is to find a long sequence for a given k, if there is any.

Input: ['2'] Output:['1 11 0']

An array of positive integers a1, a2, ..., an is given. Let us consider its arbitrary subarray al, al + 1..., ar, where 1 ≤ l ≤ r ≤ n. For every positive integer s denote by Ks the number of occurrences of s into the subarray. We call the power of the subarray the sum of products Ks·Ks·s for every positive integer s. The sum contains only finite number of nonzero summands as the number of different values in the array is indeed finite.You should calculate the power of t given subarrays.

Input: ['3 21 2 11 21 3'] Output:['36']

Physicist Woll likes to play one relaxing game in between his search of the theory of everything.Game interface consists of a rectangular n × m playing field and a dashboard. Initially some cells of the playing field are filled while others are empty. Dashboard contains images of all various connected (we mean connectivity by side) figures of 2, 3, 4 and 5 cells, with all their rotations and reflections. Player can copy any figure from the dashboard and place it anywhere at the still empty cells of the playing field. Of course any figure can be used as many times as needed.Woll's aim is to fill the whole field in such a way that there are no empty cells left, and also... just have some fun.Every initially empty cell should be filled with exactly one cell of some figure. Every figure should be entirely inside the board. In the picture black cells stand for initially filled cells of the field, and one-colour regions represent the figures.

Input: ['2 3...#.#'] Output:['000#0#']

For each positive integer n consider the integer ψ(n) which is obtained from n by replacing every digit a in the decimal notation of n with the digit (9  -  a). We say that ψ(n) is the reflection of n. For example, reflection of 192 equals 807. Note that leading zeros (if any) should be omitted. So reflection of 9 equals 0, reflection of 91 equals 8.Let us call the weight of the number the product of the number and its reflection. Thus, the weight of the number 10 is equal to 10·89 = 890.Your task is to find the maximum weight of the numbers in the given range [l, r] (boundaries are included).

Input: ['3 7'] Output:['20']

In a far away kingdom lives a very greedy king. To defend his land, he built n guard towers. Apart from the towers the kingdom has two armies, each headed by a tyrannical and narcissistic general. The generals can't stand each other, specifically, they will never let soldiers of two armies be present in one tower.During defence operations to manage a guard tower a general has to send part of his army to that tower. Each general asks some fee from the king for managing towers. As they live in a really far away kingdom, each general evaluates his fee in the following weird manner: he finds two remotest (the most distant) towers, where the soldiers of his army are situated and asks for the fee equal to the distance. Each tower is represented by a point on the plane with coordinates (x, y), and the distance between two points with coordinates (x1, y1) and (x2, y2) is determined in this kingdom as |x1 - x2| + |y1 - y2|.The greedy king was not exactly satisfied with such a requirement from the generals, that's why he only agreed to pay one fee for two generals, equal to the maximum of two demanded fees. However, the king is still green with greed, and among all the ways to arrange towers between armies, he wants to find the cheapest one. Each tower should be occupied by soldiers of exactly one army.He hired you for that. You should find the minimum amount of money that will be enough to pay the fees. And as the king is also very scrupulous, you should also count the number of arrangements that will cost the same amount of money. As their number can be quite large, it is enough for the king to know it as a remainder from dividing by 109 + 7.Two arrangements are distinct if the sets of towers occupied by soldiers of the first general are distinct.

Input: ['20 01 1'] Output:['02']

In one well-known algorithm of finding the k-th order statistics we should divide all elements into groups of five consecutive elements and find the median of each five. A median is called the middle element of a sorted array (it's the third largest element for a group of five). To increase the algorithm's performance speed on a modern video card, you should be able to find a sum of medians in each five of the array.A sum of medians of a sorted k-element set S = {a1, a2, ..., ak}, where a1 < a2 < a3 < ... < ak, will be understood by as The operator stands for taking the remainder, that is stands for the remainder of dividing x by y.To organize exercise testing quickly calculating the sum of medians for a changing set was needed.

Input: ['6add 4add 5add 1add 2add 3sum'] Output:['3']

One night, having had a hard day at work, Petya saw a nightmare. There was a binary search tree in the dream. But it was not the actual tree that scared Petya. The horrifying thing was that Petya couldn't search for elements in this tree. Petya tried many times to choose key and look for it in the tree, and each time he arrived at a wrong place. Petya has been racking his brains for long, choosing keys many times, but the result was no better. But the moment before Petya would start to despair, he had an epiphany: every time he was looking for keys, the tree didn't have the key, and occured exactly one mistake. "That's not a problem!", thought Petya. "Why not count the expectation value of an element, which is found when I search for the key". The moment he was about to do just that, however, Petya suddenly woke up.Thus, you are given a binary search tree, that is a tree containing some number written in the node. This number is called the node key. The number of children of every node of the tree is equal either to 0 or to 2. The nodes that have 0 children are called leaves and the nodes that have 2 children, are called inner. An inner node has the left child, that is the child whose key is less than the current node's key, and the right child, whose key is more than the current node's key. Also, a key of any node is strictly larger than all the keys of the left subtree of the node and strictly smaller than all the keys of the right subtree of the node.Also you are given a set of search keys, all of which are distinct and differ from the node keys contained in the tree. For each key from the set its search in the tree is realised. The search is arranged like this: initially we are located in the tree root, if the key of the current node is larger that our search key, then we move to the left child of the node, otherwise we go to the right child of the node and the process is repeated. As it is guaranteed that the search key is not contained in the tree, the search will always finish in some leaf. The key lying in the leaf is declared the search result.It is known for sure that during the search we make a mistake in comparing exactly once, that is we go the wrong way, but we won't make any mistakes later. All possible mistakes are equiprobable, that is we should consider all such searches where exactly one mistake occurs. Your task is to find the expectation (the average value) of the search result for every search key, considering that exactly one mistake occurs in the search. That is, for a set of paths containing exactly one mistake in the given key search, you should count the average value of keys containing in the leaves of those paths.

Input: ['7-1 81 41 122 22 63 103 1411'] Output:['8.0000000000']

In an embassy of a well-known kingdom an electronic queue is organised. Every person who comes to the embassy, needs to make the following three actions: show the ID, pay money to the cashier and be fingerprinted. Besides, the actions should be performed in the given order.For each action several separate windows are singled out: k1 separate windows for the first action (the first type windows), k2 windows for the second one (the second type windows), and k3 for the third one (the third type windows). The service time for one person in any of the first type window equals to t1. Similarly, it takes t2 time to serve a person in any of the second type windows. And it takes t3 to serve one person in any of the third type windows. Thus, the service time depends only on the window type and is independent from the person who is applying for visa.At some moment n people come to the embassy, the i-th person comes at the moment of time ci. The person is registered under some number. After that he sits in the hall and waits for his number to be shown on a special board. Besides the person's number the board shows the number of the window where one should go and the person goes there immediately. Let's consider that the time needed to approach the window is negligible. The table can show information for no more than one person at a time. The electronic queue works so as to immediately start working with the person who has approached the window, as there are no other people in front of the window.The Client Service Quality inspectors noticed that several people spend too much time in the embassy (this is particularly tiresome as the embassy has no mobile phone reception and 3G). It was decided to organise the system so that the largest time a person spends in the embassy were minimum. Help the inspectors organise the queue. Consider that all actions except for being served in at the window, happen instantly.

Input: ['1 1 11 1 151 1 1 1 1'] Output:['7']

Perhaps many have heard that the World Biathlon Championship has finished. Although our hero Valera was not present at this spectacular event himself and only watched it on TV, it excited him so much that he decided to enroll in a biathlon section.Of course, biathlon as any sport, proved very difficult in practice. It takes much time and effort. Workouts, workouts, and workouts, — that's what awaited Valera on his way to great achievements in biathlon.As for the workouts, you all probably know that every professional biathlete should ski fast and shoot precisely at the shooting range. Only in this case you can hope to be successful, because running and shooting are the two main components of biathlon. Valera has been diligent in his ski trainings, which is why he runs really fast, however, his shooting accuracy is nothing to write home about.On a biathlon base where Valera is preparing for the competition, there is a huge rifle range with n targets. Each target have shape of a circle, and the center of each circle is located on the Ox axis. At the last training session Valera made the total of m shots. To make monitoring of his own results easier for him, one rather well-known programmer (of course it is you) was commissioned to write a program that would reveal how many and which targets Valera hit. More specifically, for each target the program must print the number of the first successful shot (in the target), or "-1" if this was not hit. The target is considered hit if the shot is inside the circle or on its boundary. Valera is counting on you and perhaps, thanks to you he will one day win international competitions.

Input: ['32 15 210 150 11 33 04 04 0'] Output:['23 3 -1 ']

The hero of our story, Valera, and his best friend Arcady are still in school, and therefore they spend all the free time playing turn-based strategy "GAGA: Go And Go Again". The gameplay is as follows. There are two armies on the playing field each of which consists of n men (n is always even). The current player specifies for each of her soldiers an enemy's soldier he will shoot (a target) and then all the player's soldiers shot simultaneously. This is a game world, and so each soldier shoots perfectly, that is he absolutely always hits the specified target. If an enemy soldier is hit, he will surely die. It may happen that several soldiers had been indicated the same target. Killed soldiers do not participate in the game anymore. The game "GAGA" consists of three steps: first Valera makes a move, then Arcady, then Valera again and the game ends. You are asked to calculate the maximum total number of soldiers that may be killed during the game.

Input: ['2'] Output:['3']

One quite ordinary day Valera went to school (there's nowhere else he should go on a week day). In a maths lesson his favorite teacher Ms. Evans told students about divisors. Despite the fact that Valera loved math, he didn't find this particular topic interesting. Even more, it seemed so boring that he fell asleep in the middle of a lesson. And only a loud ringing of a school bell could interrupt his sweet dream. Of course, the valuable material and the teacher's explanations were lost. However, Valera will one way or another have to do the homework. As he does not know the new material absolutely, he cannot do the job himself. That's why he asked you to help. You're his best friend after all, you just cannot refuse to help. Valera's home task has only one problem, which, though formulated in a very simple way, has not a trivial solution. Its statement looks as follows: if we consider all positive integers in the interval [a;b] then it is required to count the amount of such numbers in this interval that their smallest divisor will be a certain integer k (you do not have to consider divisor equal to one). In other words, you should count the amount of such numbers from the interval [a;b], that are not divisible by any number between 2 and k - 1 and yet are divisible by k.

Input: ['1 10 2'] Output:['5']

You already know that Valery's favorite sport is biathlon. Due to your help, he learned to shoot without missing, and his skills are unmatched at the shooting range. But now a smaller task is to be performed, he should learn to complete the path fastest.The track's map is represented by a rectangle n × m in size divided into squares. Each square is marked with a lowercase Latin letter (which means the type of the plot), with the exception of the starting square (it is marked with a capital Latin letters S) and the terminating square (it is marked with a capital Latin letter T). The time of movement from one square to another is equal to 1 minute. The time of movement within the cell can be neglected. We can move from the cell only to side-adjacent ones, but it is forbidden to go beyond the map edges. Also the following restriction is imposed on the path: it is not allowed to visit more than k different types of squares (squares of one type can be visited an infinite number of times). Squares marked with S and T have no type, so they are not counted. But S must be visited exactly once — at the very beginning, and T must be visited exactly once — at the very end.Your task is to find the path from the square S to the square T that takes minimum time. Among all shortest paths you should choose the lexicographically minimal one. When comparing paths you should lexicographically represent them as a sequence of characters, that is, of plot types.

Input: ['5 3 2SbacccaaccccabT'] Output:['bcccc']

There are n animals in the queue to Dr. Dolittle. When an animal comes into the office, the doctor examines him, gives prescriptions, appoints tests and may appoint extra examination. Doc knows all the forest animals perfectly well and therefore knows exactly that the animal number i in the queue will have to visit his office exactly ai times. We will assume that an examination takes much more time than making tests and other extra procedures, and therefore we will assume that once an animal leaves the room, it immediately gets to the end of the queue to the doctor. Of course, if the animal has visited the doctor as many times as necessary, then it doesn't have to stand at the end of the queue and it immediately goes home. Doctor plans to go home after receiving k animals, and therefore what the queue will look like at that moment is important for him. Since the doctor works long hours and she can't get distracted like that after all, she asked you to figure it out.

Input: ['3 31 2 1'] Output:['2 ']

Valery is very interested in magic. Magic attracts him so much that he sees it everywhere. He explains any strange and weird phenomenon through intervention of supernatural forces. But who would have thought that even in a regular array of numbers Valera manages to see something beautiful and magical.Valera absolutely accidentally got a piece of ancient parchment on which an array of numbers was written. He immediately thought that the numbers in this array were not random. As a result of extensive research Valera worked out a wonderful property that a magical array should have: an array is defined as magic if its minimum and maximum coincide.He decided to share this outstanding discovery with you, but he asks you for help in return. Despite the tremendous intelligence and wit, Valera counts very badly and so you will have to complete his work. All you have to do is count the number of magical subarrays of the original array of numbers, written on the parchment. Subarray is defined as non-empty sequence of consecutive elements.

Input: ['42 1 1 4'] Output:['5']

Sheldon, Leonard, Penny, Rajesh and Howard are in the queue for a "Double Cola" drink vending machine; there are no other people in the queue. The first one in the queue (Sheldon) buys a can, drinks it and doubles! The resulting two Sheldons go to the end of the queue. Then the next in the queue (Leonard) buys a can, drinks it and gets to the end of the queue as two Leonards, and so on. This process continues ad infinitum.For example, Penny drinks the third can of cola and the queue will look like this: Rajesh, Howard, Sheldon, Sheldon, Leonard, Leonard, Penny, Penny.Write a program that will print the name of a man who will drink the n-th can.Note that in the very beginning the queue looks like that: Sheldon, Leonard, Penny, Rajesh, Howard. The first person is Sheldon.

Input: ['1'] Output:['Sheldon']

Polycarp loves not only to take pictures, but also to show his photos to friends. On his personal website he has recently installed a widget that can display n photos with the scroll option. At each moment of time the widget displays exactly one photograph with the option showing the previous/next one. From the first photo, you can switch to the second one or to the n-th one, from the second photo you can switch to the third one or to the first one, etc. Thus, navigation is performed in a cycle.Polycarp's collection consists of m photo albums, the i-th album contains ai photos. Polycarp wants to choose n photos and put them on a new widget. To make watching the photos interesting to the visitors, he is going to post pictures so that no two photos from one album were neighboring (each photo will have exactly two neighbors, the first photo's neighbors are the second and the n-th one).Help Polycarp compile a photo gallery. Select n photos from his collection and put them in such order that no two photos from one album went one after the other.

Input: ['4 31 3 5'] Output:['3 1 3 2']

After the educational reform Polycarp studies only two subjects at school, Safety Studies and PE (Physical Education). During the long months of the fourth term, he received n marks in them. When teachers wrote a mark in the journal, they didn't write in what subject the mark was for, they just wrote the mark.Now it's time to show the journal to his strict parents. Polycarp knows that recently at the Parent Meeting the parents were told that he received a Safety Studies marks and b PE marks (a + b = n). Now Polycarp wants to write a subject's name in front of each mark so that: there are exactly a Safety Studies marks, there are exactly b PE marks, the total average score in both subjects is maximum. An average subject grade is the sum of all marks in it, divided by the number of them. Of course, the division is performed in real numbers without rounding up or down. Polycarp aims to maximize the x1 + x2, where x1 is the average score in the first subject (Safety Studies), and x2 is the average score in the second one (Physical Education).

Input: ['53 24 4 5 4 4'] Output:['1 1 2 1 2 ']

Do you remember a kind cartoon "Beauty and the Beast"? No, no, there was no firing from machine guns or radiation mutants time-travels!There was a beauty named Belle. Once she had violated the Beast's order and visited the West Wing. After that she was banished from the castle... Everybody was upset. The beautiful Belle was upset, so was the Beast, so was Lumiere the candlestick. But the worst thing was that Cogsworth was upset. Cogsworth is not a human, but is the mantel clock, which was often used as an alarm clock.Due to Cogsworth's frustration all the inhabitants of the castle were in trouble: now they could not determine when it was time to drink morning tea, and when it was time for an evening stroll. Fortunately, deep in the basement are lying digital clock showing the time in the format HH:MM. Now the residents of the castle face a difficult task. They should turn Cogsworth's hour and minute mustache hands in such a way, that Cogsworth began to show the correct time. Moreover they need to find turn angles in degrees for each mustache hands. The initial time showed by Cogsworth is 12:00.You can only rotate the hands forward, that is, as is shown in the picture: As since there are many ways too select such angles because of full rotations, choose the smallest angles in the right (non-negative) direction.Note that Cogsworth's hour and minute mustache hands move evenly and continuously. Hands are moving independently, so when turning one hand the other hand remains standing still.

Input: ['12:00'] Output:['0 0']

A prime number is a number which has exactly two distinct divisors: one and itself. For example, numbers 2, 7, 3 are prime, and 1, 6, 4 are not.The next prime number after x is the smallest prime number greater than x. For example, the next prime number after 2 is 3, and the next prime number after 3 is 5. Note that there is exactly one next prime number after each number. So 5 is not the next prime number for 2.One cold April morning Panoramix predicted that soon Kakofonix will break free from his straitjacket, and this will be a black day for the residents of the Gallic countryside.Panoramix's prophecy tells that if some day Asterix and Obelix beat exactly x Roman soldiers, where x is a prime number, and next day they beat exactly y Roman soldiers, where y is the next prime number after x, then it's time to wait for Armageddon, for nothing can shut Kakofonix up while he sings his infernal song.Yesterday the Gauls beat n Roman soldiers and it turned out that the number n was prime! Today their victims were a troop of m Romans (m > n). Determine whether the Gauls should wait for the black day after today's victory of Asterix and Obelix?

Input: ['3 5'] Output:['YES']

Fox Ciel safely returned to her castle, but there was something wrong with the security system of the castle: sensors attached in the castle were covering her.Ciel is at point (1, 1) of the castle now, and wants to move to point (n, n), which is the position of her room. By one step, Ciel can move from point (x, y) to either (x + 1, y) (rightward) or (x, y + 1) (upward).In her castle, c2 sensors are set at points (a + i, b + j) (for every integer i and j such that: 0 ≤ i < c, 0 ≤ j < c).Each sensor has a count value and decreases its count value every time Ciel moves. Initially, the count value of each sensor is t. Every time Ciel moves to point (x, y), the count value of a sensor at point (u, v) decreases by (|u - x| + |v - y|). When the count value of some sensor becomes strictly less than 0, the sensor will catch Ciel as a suspicious individual!Determine whether Ciel can move from (1, 1) to (n, n) without being caught by a sensor, and if it is possible, output her steps. Assume that Ciel can move to every point even if there is a censor on the point.

Input: ['5 25 2 4 1'] Output:['RRUURURU']

After Fox Ciel got off a bus, she found that the bus she was on was a wrong bus and she lost her way in a strange town. However, she fortunately met her friend Beaver Taro and asked which way to go to her castle. Taro's response to her was a string s, and she tried to remember the string s correctly.However, Ciel feels n strings b1, b2, ... , bn are really boring, and unfortunately she dislikes to remember a string that contains a boring substring. To make the thing worse, what she can remember is only the contiguous substring of s.Determine the longest contiguous substring of s that does not contain any boring string, so that she can remember the longest part of Taro's response.

Input: ['Go_straight_along_this_street5strlongtreebigintegerellipse'] Output:['12 4']

After Fox Ciel won an onsite round of a programming contest, she took a bus to return to her castle. The fee of the bus was 220 yen. She met Rabbit Hanako in the bus. They decided to play the following game because they got bored in the bus. Initially, there is a pile that contains x 100-yen coins and y 10-yen coins. They take turns alternatively. Ciel takes the first turn. In each turn, they must take exactly 220 yen from the pile. In Ciel's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 100-yen coins. In Hanako's turn, if there are multiple ways to take 220 yen, she will choose the way that contains the maximal number of 10-yen coins. If Ciel or Hanako can't take exactly 220 yen from the pile, she loses. Determine the winner of the game.

Input: ['2 2'] Output:['Ciel']

A breakthrough among computer games, "Civilization XIII", is striking in its scale and elaborate details. Let's take a closer look at one of them.The playing area in the game is split into congruent cells that are regular hexagons. The side of each cell is equal to 1. Each unit occupies exactly one cell of the playing field. The field can be considered infinite. Let's take a look at the battle unit called an "Archer". Each archer has a parameter "shot range". It's a positive integer that determines the radius of the circle in which the archer can hit a target. The center of the circle coincides with the center of the cell in which the archer stays. A cell is considered to be under the archer’s fire if and only if all points of this cell, including border points are located inside the circle or on its border.The picture below shows the borders for shot ranges equal to 3, 4 and 5. The archer is depicted as A. Find the number of cells that are under fire for some archer.

Input: ['3'] Output:['7']

"Eat a beaver, save a tree!" — That will be the motto of ecologists' urgent meeting in Beaverley Hills.And the whole point is that the population of beavers on the Earth has reached incredible sizes! Each day their number increases in several times and they don't even realize how much their unhealthy obsession with trees harms the nature and the humankind. The amount of oxygen in the atmosphere has dropped to 17 per cent and, as the best minds of the world think, that is not the end.In the middle of the 50-s of the previous century a group of soviet scientists succeed in foreseeing the situation with beavers and worked out a secret technology to clean territory. The technology bears a mysterious title "Beavermuncher-0xFF". Now the fate of the planet lies on the fragile shoulders of a small group of people who has dedicated their lives to science.The prototype is ready, you now need to urgently carry out its experiments in practice. You are given a tree, completely occupied by beavers. A tree is a connected undirected graph without cycles. The tree consists of n vertices, the i-th vertex contains ki beavers. "Beavermuncher-0xFF" works by the following principle: being at some vertex u, it can go to the vertex v, if they are connected by an edge, and eat exactly one beaver located at the vertex v. It is impossible to move to the vertex v if there are no beavers left in v. "Beavermuncher-0xFF" cannot just stand at some vertex and eat beavers in it. "Beavermuncher-0xFF" must move without stops.Why does the "Beavermuncher-0xFF" works like this? Because the developers have not provided place for the battery in it and eating beavers is necessary for converting their mass into pure energy.It is guaranteed that the beavers will be shocked by what is happening, which is why they will not be able to move from a vertex of the tree to another one. As for the "Beavermuncher-0xFF", it can move along each edge in both directions while conditions described above are fulfilled.The root of the tree is located at the vertex s. This means that the "Beavermuncher-0xFF" begins its mission at the vertex s and it must return there at the end of experiment, because no one is going to take it down from a high place. Determine the maximum number of beavers "Beavermuncher-0xFF" can eat and return to the starting vertex.

Input: ['51 3 1 3 22 53 44 51 54'] Output:['6']

For some reason in many American cartoons anvils fall from time to time onto heroes' heads. Of course, safes, wardrobes, cruisers, planes fall sometimes too... But anvils do so most of all.Anvils come in different sizes and shapes. Quite often they get the hero stuck deep in the ground. But have you ever thought who throws anvils from the sky? From what height? We are sure that such questions have never troubled you!It turns out that throwing an anvil properly is not an easy task at all. Let's describe one of the most popular anvil throwing models.Let the height p of the potential victim vary in the range [0;a] and the direction of the wind q vary in the range [ - b;b]. p and q could be any real (floating) numbers. Then we can assume that the anvil will fit the toon's head perfectly only if the following equation has at least one real root: Determine the probability with which an aim can be successfully hit by an anvil.You can assume that the p and q coefficients are chosen equiprobably and independently in their ranges.

Input: ['24 21 2'] Output:['0.62500000000.5312500000']

The year of 2012 is coming...According to an ancient choradrican legend in this very year, in 2012, Diablo and his brothers Mephisto and Baal will escape from hell, and innumerable hordes of demons will enslave the human world. But seven brave heroes have already gathered on the top of a mountain Arreat to protect us mere mortals from the effect of this terrible evil.The seven great heroes are: amazon Anka, barbarian Chapay, sorceress Cleo, druid Troll, necromancer Dracul, paladin Snowy and a professional hit girl Hexadecimal. Heroes already know how much experience will be given for each of the three megabosses: a for Mephisto, b for Diablo and c for Baal.Here's the problem: heroes are as much as seven and megabosses are only three! Then our heroes decided to split into three teams, where each team will go to destroy their own megaboss. Each team member will receive a of experience, rounded down, where x will be the amount of experience for the killed megaboss and y — the number of people in the team.Heroes do not want to hurt each other's feelings, so they want to split into teams so that the difference between the hero who received the maximum number of experience and the hero who received the minimum number of experience were minimal. Since there can be several divisions into teams, then you need to find the one in which the total amount of liking in teams were maximum.It is known that some heroes like others. But if hero p likes hero q, this does not mean that the hero q likes hero p. No hero likes himself.The total amount of liking in teams is the amount of ordered pairs (p, q), such that heroes p and q are in the same group, and hero p likes hero q (but it is not important if hero q likes hero p). In case of heroes p and q likes each other and they are in the same group, this pair should be counted twice, as (p, q) and (q, p).A team can consist even of a single hero, but it is important that every megaboss was destroyed. All heroes must be involved in the campaign against evil. None of the heroes can be in more than one team.It is guaranteed that every hero is able to destroy any megaboss alone.

Input: ['3Troll likes DraculDracul likes AnkaSnowy likes Hexadecimal210 200 180'] Output:['30 3']

Tourist walks along the X axis. He can choose either of two directions and any speed not exceeding V. He can also stand without moving anywhere. He knows from newspapers that at time t1 in the point with coordinate x1 an interesting event will occur, at time t2 in the point with coordinate x2 — another one, and so on up to (xn, tn). Interesting events are short so we can assume they are immediate. Event i counts visited if at time ti tourist was at point with coordinate xi.Write program tourist that will find maximum number of events tourist if: at the beginning (when time is equal to 0) tourist appears at point 0, tourist can choose initial point for himself. Yes, you should answer on two similar but different questions.

Input: ['3-1 142 740 82'] Output:['1 2']

You are given N points on a plane. Write a program which will find the sum of squares of distances between all pairs of points.

Input: ['41 1-1 -11 -1-1 1'] Output:['32']

Bitwise exclusive OR (or bitwise addition modulo two) is a binary operation which is equivalent to applying logical exclusive OR to every pair of bits located on the same positions in binary notation of operands. In other words, a binary digit of the result is equal to 1 if and only if bits on the respective positions in the operands are different.For example, if X = 10910 = 11011012, Y = 4110 = 1010012, then: X xor Y  =  6810  =  10001002. Write a program, which takes two non-negative integers A and B as an input and finds two non-negative integers X and Y, which satisfy the following conditions: A = X + Y B  =  X xor Y, where xor is bitwise exclusive or. X is the smallest number among all numbers for which the first two conditions are true.

Input: ['14276'] Output:['33 109']

Scientists of planet Olympia are conducting an experiment in mutation of primitive organisms. Genome of organism from this planet can be represented as a string of the first K capital English letters. For each pair of types of genes they assigned ai, j — a risk of disease occurence in the organism provided that genes of these types are adjacent in the genome, where i — the 1-based index of the first gene and j — the index of the second gene. The gene 'A' has index 1, 'B' has index 2 and so on. For example, a3, 2 stands for the risk of 'CB' fragment. Risk of disease occurence in the organism is equal to the sum of risks for each pair of adjacent genes in the genome.Scientists have already obtained a base organism. Some new organisms can be obtained by mutation of this organism. Mutation involves removal of all genes of some particular types. Such removal increases the total risk of disease occurence additionally. For each type of genes scientists determined ti — the increasement of the total risk of disease occurence provided by removal of all genes having type with index i. For example, t4 stands for the value of additional total risk increasement in case of removing all the 'D' genes.Scientists want to find a number of different organisms that can be obtained from the given one which have the total risk of disease occurence not greater than T. They can use only the process of mutation described above. Two organisms are considered different if strings representing their genomes are different. Genome should contain at least one gene.

Input: ['5 3 13BACAC4 1 21 2 32 3 43 4 10'] Output:['5']

Modern researches has shown that a flock of hungry mice searching for a piece of cheese acts as follows: if there are several pieces of cheese then each mouse chooses the closest one. After that all mice start moving towards the chosen piece of cheese. When a mouse or several mice achieve the destination point and there is still a piece of cheese in it, they eat it and become well-fed. Each mice that reaches this point after that remains hungry. Moving speeds of all mice are equal.If there are several ways to choose closest pieces then mice will choose it in a way that would minimize the number of hungry mice. To check this theory scientists decided to conduct an experiment. They located N mice and M pieces of cheese on a cartesian plane where all mice are located on the line y = Y0 and all pieces of cheese — on another line y = Y1. To check the results of the experiment the scientists need a program which simulates the behavior of a flock of hungry mice.Write a program that computes the minimal number of mice which will remain hungry, i.e. without cheese.

Input: ['3 2 0 20 1 32 5'] Output:['1']

Ahmed and Mostafa used to compete together in many programming contests for several years. Their coach Fegla asked them to solve one challenging problem, of course Ahmed was able to solve it but Mostafa couldn't.This problem is similar to a standard problem but it has a different format and constraints.In the standard problem you are given an array of integers, and you have to find one or more consecutive elements in this array where their sum is the maximum possible sum.But in this problem you are given n small arrays, and you will create one big array from the concatenation of one or more instances of the small arrays (each small array could occur more than once). The big array will be given as an array of indexes (1-based) of the small arrays, and the concatenation should be done in the same order as in this array. Then you should apply the standard problem mentioned above on the resulting big array.For example let's suppose that the small arrays are {1, 6, -2}, {3, 3} and {-5, 1}. And the indexes in the big array are {2, 3, 1, 3}. So the actual values in the big array after formatting it as concatenation of the small arrays will be {3, 3, -5, 1, 1, 6, -2, -5, 1}. In this example the maximum sum is 9.Can you help Mostafa solve this problem?

Input: ['3 43 1 6 -22 3 32 -5 12 3 1 3'] Output:['9']

Well, here is another math class task. In mathematics, GCD is the greatest common divisor, and it's an easy task to calculate the GCD between two positive integers.A common divisor for two positive numbers is a number which both numbers are divisible by.But your teacher wants to give you a harder task, in this task you have to find the greatest common divisor d between two integers a and b that is in a given range from low to high (inclusive), i.e. low ≤ d ≤ high. It is possible that there is no common divisor in the given range.You will be given the two integers a and b, then n queries. Each query is a range from low to high and you have to answer each query.

Input: ['9 2731 510 119 11'] Output:['3-19']

Vasya plays the Plane of Tanks. The tanks in this game keep trying to finish each other off. But your "Pedalny" is not like that... He just needs to drive in a straight line from point A to point B on the plane. Unfortunately, on the same plane are n enemy tanks. We shall regard all the tanks as points. At the initial moment of time Pedalny is at the point A. Enemy tanks would be happy to destroy it immediately, but initially their turrets are tuned in other directions. Specifically, for each tank we know the initial rotation of the turret ai (the angle in radians relative to the OX axis in the counterclockwise direction) and the maximum speed of rotation of the turret wi (radians per second). If at any point of time a tank turret will be aimed precisely at the tank Pedalny, then the enemy fires and it never misses. Pedalny can endure no more than k shots. Gun reloading takes very much time, so we can assume that every enemy will produce no more than one shot. Your task is to determine what minimum speed of v Pedalny must have to get to the point B. It is believed that Pedalny is able to instantly develop the speed of v, and the first k shots at him do not reduce the speed and do not change the coordinates of the tank.

Input: ['0 0 10 015 -5 4.71238 10'] Output:['4.2441']

Vasya plays FreeDiv. In this game he manages a huge state, which has n cities and m two-way roads between them. Unfortunately, not from every city you can reach any other one moving along these roads. Therefore Vasya decided to divide the state into provinces so that in every province, one could reach from every city all the cities of the province, but there are no roads between provinces. Unlike other turn-based strategies, in FreeDiv a player has the opportunity to build tunnels between cities. The tunnels are two-way roads along which one can move armies undetected by the enemy. However, no more than one tunnel can be connected to each city. As for Vasya, he wants to build a network of tunnels so that any pair of cities in his state were reachable by some path consisting of roads and a tunnels. But at that no more than k tunnels are connected to each province (otherwise, the province will be difficult to keep in case other provinces are captured by enemy armies).Vasya discovered that maybe he will not be able to build such a network for the current condition of the state. Maybe he'll have first to build several roads between cities in different provinces to merge the provinces. Your task is to determine the minimum number of roads Vasya needs to build so that it was possible to build the required network of tunnels in the resulting state.

Input: ['3 3 21 22 33 1'] Output:['0']

After the nationalization of the oil industry, Dr. Mosaddegh wants to dig some oil wells to extract all the oil in Persian Gulf. But Persian Gulf is huge and has an infinite amount of oil. So Dr. Mosaddegh works only on a rectangular plane of size n × m of the Persian Gulf. Each of the cells in this rectangle either contains an infinite amount of oil or nothing.Two cells are considered adjacent if and only if they have a common edge, a path is a sequence c1, c2, ..., cx of cells so that all of them contain oil and for each i, ci is adjacent to ci - 1 and ci + 1 (if they exist). Two cells are considered connected to each other if and only if there exists a path between them. If we dig a well in a certain cell, we can extract oil from all the cells that are connected to it by oil paths. It is not allowed to dig wells on empty cells.Dr. Mosaddegh also knows that in Persian Gulf, the empty cells form rows and columns. I. e. if some cell is empty, then it's column is completely empty or it's row is completely empty, or both.Help Dr. Mosaddegh find out how many wells he has to dig to access all the oil in that region.

Input: ['2 31 21 2'] Output:['2']

Ali Koochooloo is going to buy new clothes since we're reaching Noruz, the ancient Persian festival and the beginning of new Persian year.When Ali entered a shop, he saw that the shopkeeper was a programmer and since there is no money in programming he had changed his career. The shopkeeper told Ali that he can buy anything for free if he could answer a simple question in 10 seconds. But to see the question Ali has to pay 3 tomans.Ali agreed instantly and the shopkeeper handed him a piece of paper containing the task. The task was indeed very simple. It said: Let string A be ababababababab. Which non-empty substring of A is repeated the most times in it?Ali answered fast. He said the answer is a. But the shopkeeper said that Ali is wrong and asked him to read the rest of statement:If several substrings have the maximal repeat time, then the substring with maximal length would be the answer, in case of a tie the alphabetically latest substring will be chosen.So the answer is ab.Now Ali wants us to solve this problem for different strings. We don't have a great advantage over Ali, we just have a computer and a weird language.

Input: ['abab'] Output:['ab']

The positive integer a is a divisor of the positive integer b if and only if there exists a positive integer c such that a × c = b. King Astyages thinks a positive integer x is extraordinarily nice if the number of its even divisors is equal to the number of its odd divisors.For example 3 has two positive divisors 3 and 1, both of which are odd, so 3 is not extraordinarily nice. On the other hand 2 is only divisible by 2 and 1, so it has one odd and one even divisor. Therefore 2 is extraordinarily nice.Given a positive integer x determine whether it's extraordinarily nice.

Input: ['2'] Output:['yes']

Goshtasp was known to be a good programmer in his school. One day Vishtasp, Goshtasp's friend, asked him to solve this task:Given a positive integer n, you should determine whether n is rich.The positive integer x is rich, if there exists some set of distinct numbers a1, a2, ..., am such that . In addition: every ai should be either a prime number, or equal to 1.Vishtasp said that he would share his Eidi 50 / 50 with Goshtasp, if he could solve the task. Eidi is money given to children for Noruz by their parents and/or relatives.Goshtasp needs to solve this problem to get money, you need to solve it to get score!

Input: ['11'] Output:['11=11']

Vasya has a pack of 54 cards (52 standard cards and 2 distinct jokers). That is all he has at the moment. Not to die from boredom, Vasya plays Solitaire with them.Vasya lays out nm cards as a rectangle n × m. If there are jokers among them, then Vasya should change them with some of the rest of 54 - nm cards (which are not layed out) so that there were no jokers left. Vasya can pick the cards to replace the jokers arbitrarily. Remember, that each card presents in pack exactly once (i. e. in a single copy). Vasya tries to perform the replacements so that the solitaire was solved.Vasya thinks that the solitaire is solved if after the jokers are replaced, there exist two non-overlapping squares 3 × 3, inside each of which all the cards either have the same suit, or pairwise different ranks.Determine by the initial position whether the solitaire can be solved or not. If it can be solved, show the way in which it is possible.

Input: ['4 62S 3S 4S 7S 8S AS5H 6H 7H 5S TC AC8H 9H TH 7C 8C 9C2D 2C 3C 4C 5C 6C'] Output:['No solution.']

There are n knights sitting at the Round Table at an equal distance from each other. Each of them is either in a good or in a bad mood.Merlin, the wizard predicted to King Arthur that the next month will turn out to be particularly fortunate if the regular polygon can be found. On all vertices of the polygon knights in a good mood should be located. Otherwise, the next month will bring misfortunes.A convex polygon is regular if all its sides have same length and all his angles are equal. In this problem we consider only regular polygons with at least 3 vertices, i. e. only nondegenerated.On a picture below some examples of such polygons are present. Green points mean knights in a good mood. Red points mean ones in a bad mood. King Arthur knows the knights' moods. Help him find out if the next month will be fortunate or not.

Input: ['31 1 1'] Output:['YES']

A progress bar is an element of graphical interface that displays the progress of a process for this very moment before it is completed. Let's take a look at the following form of such a bar.A bar is represented as n squares, located in line. To add clarity, let's number them with positive integers from 1 to n from the left to the right. Each square has saturation (ai for the i-th square), which is measured by an integer from 0 to k. When the bar for some i (1 ≤ i ≤ n) is displayed, squares 1, 2, ... , i - 1 has the saturation k, squares i + 1, i + 2, ... , n has the saturation 0, and the saturation of the square i can have any value from 0 to k.So some first squares of the progress bar always have the saturation k. Some last squares always have the saturation 0. And there is no more than one square that has the saturation different from 0 and k.The degree of the process's completion is measured in percents. Let the process be t% completed. Then the following inequation is fulfilled: An example of such a bar can be seen on the picture. For the given n, k, t determine the measures of saturation for all the squares ai of the progress bar.

Input: ['10 10 54'] Output:['10 10 10 10 10 4 0 0 0 0 ']

In Walrusland public transport tickets are characterized by two integers: by the number of the series and by the number of the ticket in the series. Let the series number be represented by a and the ticket number — by b, then a ticket is described by the ordered pair of numbers (a, b). The walruses believe that a ticket is lucky if a * b = rev(a) * rev(b). The function rev(x) reverses a number written in the decimal system, at that the leading zeroes disappear. For example, rev(12343) = 34321, rev(1200) = 21.The Public Transport Management Committee wants to release x series, each containing y tickets, so that at least w lucky tickets were released and the total number of released tickets (x * y) were minimum. The series are numbered from 1 to x inclusive. The tickets in each series are numbered from 1 to y inclusive. The Transport Committee cannot release more than maxx series and more than maxy tickets in one series.

Input: ['2 2 1'] Output:['1 1']

Fangy the little walrus, as all the modern walruses, loves to communicate via text messaging. One day he faced the following problem: When he sends large texts, they are split into parts each containing n characters (which is the size of one text message). Thus, whole sentences and words get split!Fangy did not like it, so he faced the task of breaking the text into minimal messages on his own so that no sentence were broken into pieces when it is sent and the number of text messages to be sent would be minimal. If two consecutive sentences are in different messages, the space between them can be ignored (Fangy does not write this space).The little walrus's text looks in the following manner: TEXT ::= SENTENCE | SENTENCE SPACE TEXTSENTENCE ::= WORD SPACE SENTENCE | WORD ENDEND ::= {'.', '?', '!'}WORD ::= LETTER | LETTER WORDLETTER ::= {'a'..'z', 'A'..'Z'}SPACE ::= ' 'SPACE stands for the symbol of a space.So, how many messages did Fangy send?

Input: ['25Hello. I am a little walrus.'] Output:['2']

Fangy collects cookies. Once he decided to take a box and put cookies into it in some way. If we take a square k × k in size, divided into blocks 1 × 1 in size and paint there the main diagonal together with cells, which lie above it, then the painted area will be equal to the area occupied by one cookie k in size. Fangy also has a box with a square base 2n × 2n, divided into blocks 1 × 1 in size. In a box the cookies should not overlap, and they should not be turned over or rotated. See cookies of sizes 2 and 4 respectively on the figure: To stack the cookies the little walrus uses the following algorithm. He takes out of the repository the largest cookie which can fit in some place in the box and puts it there. Everything could be perfect but alas, in the repository the little walrus has infinitely many cookies of size 2 and larger, and there are no cookies of size 1, therefore, empty cells will remain in the box. Fangy wants to know how many empty cells will be left in the end.

Input: ['3'] Output:['9']

In Chelyabinsk lives a much respected businessman Nikita with a strange nickname "Boss". Once Nikita decided to go with his friend Alex to the Summer Biathlon World Cup. Nikita, as a very important person, received a token which allows to place bets on each section no more than on one competitor.To begin with friends learned the rules: in the race there are n sections of equal length and m participants. The participants numbered from 1 to m. About each participant the following is known: li — the number of the starting section, ri — the number of the finishing section (li ≤ ri), ti — the time a biathlete needs to complete an section of the path, ci — the profit in roubles. If the i-th sportsman wins on one of the sections, the profit will be given to the man who had placed a bet on that sportsman. The i-th biathlete passes the sections from li to ri inclusive. The competitor runs the whole way in (ri - li + 1)·ti time units. It takes him exactly ti time units to pass each section. In case of the athlete's victory on k sections the man who has betted on him receives k·ci roubles.In each section the winner is determined independently as follows: if there is at least one biathlete running this in this section, then among all of them the winner is the one who has ran this section in minimum time (spent minimum time passing this section). In case of equality of times the athlete with the smaller index number wins. If there are no participants in this section, then the winner in this section in not determined. We have to say that in the summer biathlon all the participants are moving at a constant speed.We should also add that Nikita can bet on each section and on any contestant running in this section.Help the friends find the maximum possible profit.

Input: ['4 41 4 20 51 3 21 103 3 4 303 4 4 20'] Output:['60']

A guy named Vasya attends the final grade of a high school. One day Vasya decided to watch a match of his favorite hockey team. And, as the boy loves hockey very much, even more than physics, he forgot to do the homework. Specifically, he forgot to complete his physics tasks. Next day the teacher got very angry at Vasya and decided to teach him a lesson. He gave the lazy student a seemingly easy task: You are given an idle body in space and the forces that affect it. The body can be considered as a material point with coordinates (0; 0; 0). Vasya had only to answer whether it is in equilibrium. "Piece of cake" — thought Vasya, we need only to check if the sum of all vectors is equal to 0. So, Vasya began to solve the problem. But later it turned out that there can be lots and lots of these forces, and Vasya can not cope without your help. Help him. Write a program that determines whether a body is idle or is moving by the given vectors of forces.

Input: ['34 1 7-2 4 -11 -5 -3'] Output:['NO']

Recently Petya has become keen on physics. Anna V., his teacher noticed Petya's interest and gave him a fascinating physical puzzle — a half-decay tree. A half-decay tree is a complete binary tree with the height h. The height of a tree is the length of the path (in edges) from the root to a leaf in the tree. While studying the tree Petya can add electrons to vertices or induce random decay with synchrophasotron. Random decay is a process during which the edges of some path from the root to the random leaf of the tree are deleted. All the leaves are equiprobable. As the half-decay tree is the school property, Petya will return back the deleted edges into the tree after each decay.After being desintegrated, the tree decomposes into connected components. Charge of each component is the total quantity of electrons placed in vertices of the component. Potential of desintegerated tree is the maximum from the charges of its connected components. Each time before inducing random decay Petya is curious about the mathematical expectation of potential of the tree after being desintegrated.

Input: ['1 4add 1 3add 2 10add 3 11decay'] Output:['13.50000000']

For some experiments little Petya needs a synchrophasotron. He has already got the device, all that's left is to set the fuel supply. Fuel comes through a system of nodes numbered from 1 to n and connected by pipes. Pipes go from every node with smaller number to every node with greater number. Fuel can only flow through pipes in direction from node with smaller number to node with greater number. Any amount of fuel can enter through the first node and the last node is connected directly to the synchrophasotron. It is known that every pipe has three attributes: the minimum amount of fuel that should go through it, the maximum amount of fuel that can possibly go through it and the cost of pipe activation. If cij units of fuel (cij > 0) flow from node i to node j, it will cost aij + cij2 tugriks (aij is the cost of pipe activation), and if fuel doesn't flow through the pipe, it doesn't cost anything. Only integer number of units of fuel can flow through each pipe.Constraints on the minimal and the maximal fuel capacity of a pipe take place always, not only if it is active. You may assume that the pipe is active if and only if the flow through it is strictly greater than zero.Petya doesn't want the pipe system to be overloaded, so he wants to find the minimal amount of fuel, that, having entered the first node, can reach the synchrophasotron. Besides that he wants to impress the sponsors, so the sum of money needed to be paid for fuel to go through each pipe, must be as big as possible.

Input: ['21 2 1 2 3'] Output:['1 4']

It is well known that the planet suffers from the energy crisis. Little Petya doesn't like that and wants to save the world. For this purpose he needs every accumulator to contain the same amount of energy. Initially every accumulator has some amount of energy: the i-th accumulator has ai units of energy. Energy can be transferred from one accumulator to the other. Every time x units of energy are transferred (x is not necessarily an integer) k percent of it is lost. That is, if x units were transferred from one accumulator to the other, amount of energy in the first one decreased by x units and in other increased by units.Your task is to help Petya find what maximum equal amount of energy can be stored in each accumulator after the transfers.

Input: ['3 504 2 1'] Output:['2.000000000']

Professor Phunsuk Wangdu has performed some experiments on rays. The setup for n rays is as follows.There is a rectangular box having exactly n holes on the opposite faces. All rays enter from the holes of the first side and exit from the holes of the other side of the box. Exactly one ray can enter or exit from each hole. The holes are in a straight line. Professor Wangdu is showing his experiment to his students. He shows that there are cases, when all the rays are intersected by every other ray. A curious student asked the professor: "Sir, there are some groups of rays such that all rays in that group intersect every other ray in that group. Can we determine the number of rays in the largest of such groups?".Professor Wangdu now is in trouble and knowing your intellect he asks you to help him.

Input: ['51 4 5 2 33 4 2 1 5'] Output:['3']

Let A = {a1, a2, ..., an} be any permutation of the first n natural numbers {1, 2, ..., n}. You are given a positive integer k and another sequence B = {b1, b2, ..., bn}, where bi is the number of elements aj in A to the left of the element at = i such that aj ≥ (i + k).For example, if n = 5, a possible A is {5, 1, 4, 2, 3}. For k = 2, B is given by {1, 2, 1, 0, 0}. But if k = 3, then B = {1, 1, 0, 0, 0}.For two sequences X = {x1, x2, ..., xn} and Y = {y1, y2, ..., yn}, let i-th elements be the first elements such that xi ≠ yi. If xi < yi, then X is lexicographically smaller than Y, while if xi > yi, then X is lexicographically greater than Y.Given n, k and B, you need to determine the lexicographically smallest A.

Input: ['5 21 2 1 0 0'] Output:['4 1 5 2 3 ']

A teacher decides to give toffees to his students. He asks n students to stand in a queue. Since the teacher is very partial, he follows the following rule to distribute toffees.He looks at the first two students and gives more toffees to the student having higher marks than the other one. If they have the same marks they get the same number of toffees. The same procedure is followed for each pair of adjacent students starting from the first one to the last one.It is given that each student receives at least one toffee. You have to find the number of toffees given to each student by the teacher such that the total number of toffees is minimum.

Input: ['5LRLR'] Output:['2 1 2 1 2']

Little Petya has a birthday soon. Due this wonderful event, Petya's friends decided to give him sweets. The total number of Petya's friends equals to n.Let us remind you the definition of the greatest common divisor: GCD(a1, ..., ak) = d, where d represents such a maximal positive number that each ai (1 ≤ i ≤ k) is evenly divisible by d. At that, we assume that all ai's are greater than zero.Knowing that Petya is keen on programming, his friends has agreed beforehand that the 1-st friend gives a1 sweets, the 2-nd one gives a2 sweets, ..., the n-th one gives an sweets. At the same time, for any i and j (1 ≤ i, j ≤ n) they want the GCD(ai, aj) not to be equal to 1. However, they also want the following condition to be satisfied: GCD(a1, a2, ..., an) = 1. One more: all the ai should be distinct.Help the friends to choose the suitable numbers a1, ..., an.

Input: ['3'] Output:['995511115']

Little Petya often travels to his grandmother in the countryside. The grandmother has a large garden, which can be represented as a rectangle 1 × n in size, when viewed from above. This rectangle is divided into n equal square sections. The garden is very unusual as each of the square sections possesses its own fixed height and due to the newest irrigation system we can create artificial rain above each section.Creating artificial rain is an expensive operation. That's why we limit ourselves to creating the artificial rain only above one section. At that, the water from each watered section will flow into its neighbouring sections if their height does not exceed the height of the section. That is, for example, the garden can be represented by a 1 × 5 rectangle, where the section heights are equal to 4, 2, 3, 3, 2. Then if we create an artificial rain over any of the sections with the height of 3, the water will flow over all the sections, except the ones with the height of 4. See the illustration of this example at the picture: As Petya is keen on programming, he decided to find such a section that if we create artificial rain above it, the number of watered sections will be maximal. Help him.

Input: ['12'] Output:['1']

As you know, Hogwarts has four houses: Gryffindor, Hufflepuff, Ravenclaw and Slytherin. The sorting of the first-years into houses is done by the Sorting Hat. The pupils are called one by one in the alphabetical order, each of them should put a hat on his head and, after some thought, the hat solemnly announces the name of the house the student should enter.At that the Hat is believed to base its considerations on the student's personal qualities: it sends the brave and noble ones to Gryffindor, the smart and shrewd ones — to Ravenclaw, the persistent and honest ones — to Hufflepuff and the clever and cunning ones — to Slytherin. However, a first year student Hermione Granger got very concerned about the forthcoming sorting. She studied all the literature on the Sorting Hat and came to the conclusion that it is much simpler than that. If the relatives of the student have already studied at Hogwarts, the hat puts the student to the same house, where his family used to study. In controversial situations, when the relatives studied in different houses or when they were all Muggles like Hermione's parents, then the Hat sorts the student to the house, to which the least number of first years has been sent at that moment. If there are several such houses, the choice is given to the student himself. Then the student can choose any of the houses, to which the least number of first years has been sent so far. Hermione has already asked the students that are on the list before her about their relatives. Now she and her new friends Harry Potter and Ron Weasley want to find out into what house the Hat will put Hermione.

Input: ['11G????SS???H'] Output:['GryffindorRavenclaw']

Brothers Fred and George Weasley once got into the sporting goods store and opened a box of Quidditch balls. After long and painful experiments they found out that the Golden Snitch is not enchanted at all. It is simply a programmed device. It always moves along the same trajectory, which is a polyline with vertices at the points (x0, y0, z0), (x1, y1, z1), ..., (xn, yn, zn). At the beginning of the game the snitch is positioned at the point (x0, y0, z0), and then moves along the polyline at the constant speed vs. The twins have not yet found out how the snitch behaves then. Nevertheless, they hope that the retrieved information will help Harry Potter and his team in the upcoming match against Slytherin. Harry Potter learned that at the beginning the game he will be at the point (Px, Py, Pz) and his super fast Nimbus 2011 broom allows him to move at the constant speed vp in any direction or remain idle. vp is not less than the speed of the snitch vs. Harry Potter, of course, wants to catch the snitch as soon as possible. Or, if catching the snitch while it is moving along the polyline is impossible, he wants to hurry the Weasley brothers with their experiments. Harry Potter catches the snitch at the time when they are at the same point. Help Harry.

Input: ['40 0 00 10 010 10 010 0 00 0 01 15 5 25'] Output:['YES25.500000000010.0000000000 4.5000000000 0.0000000000']

The History of Magic is perhaps the most boring subject in the Hogwarts school of Witchcraft and Wizardry. Harry Potter is usually asleep during history lessons, and his magical quill writes the lectures for him. Professor Binns, the history of magic teacher, lectures in such a boring and monotonous voice, that he has a soporific effect even on the quill. That's why the quill often makes mistakes, especially in dates.So, at the end of the semester Professor Binns decided to collect the students' parchments with notes and check them. Ron Weasley is in a panic: Harry's notes may contain errors, but at least he has some notes, whereas Ron does not have any. Ronald also has been sleeping during the lectures and his quill had been eaten by his rat Scabbers. Hermione Granger refused to give Ron her notes, because, in her opinion, everyone should learn on their own. Therefore, Ron has no choice but to copy Harry's notes.Due to the quill's errors Harry's dates are absolutely confused: the years of goblin rebellions and other important events for the wizarding world do not follow in order, and sometimes even dates from the future occur. Now Ron wants to change some of the digits while he copies the notes so that the dates were in the chronological (i.e. non-decreasing) order and so that the notes did not have any dates strictly later than 2011, or strictly before than 1000. To make the resulting sequence as close as possible to the one dictated by Professor Binns, Ron will change no more than one digit in each date into other digit. Help him do it.

Input: ['3187519361721'] Output:['183518361921']

A long time ago (probably even in the first book), Nicholas Flamel, a great alchemist and the creator of the Philosopher's Stone, taught Harry Potter three useful spells. The first one allows you to convert a grams of sand into b grams of lead, the second one allows you to convert c grams of lead into d grams of gold and third one allows you to convert e grams of gold into f grams of sand. When Harry told his friends about these spells, Ron Weasley was amazed. After all, if they succeed in turning sand into lead, lead into gold, and then turning part of the gold into sand again and so on, then it will be possible to start with a small amount of sand and get huge amounts of gold! Even an infinite amount of gold! Hermione Granger, by contrast, was skeptical about that idea. She argues that according to the law of conservation of matter getting an infinite amount of matter, even using magic, is impossible. On the contrary, the amount of matter may even decrease during transformation, being converted to magical energy. Though Hermione's theory seems convincing, Ron won't believe her. As far as Ron is concerned, Hermione made up her law of conservation of matter to stop Harry and Ron wasting their time with this nonsense, and to make them go and do homework instead. That's why Ron has already collected a certain amount of sand for the experiments. A quarrel between the friends seems unavoidable...Help Harry to determine which one of his friends is right, and avoid the quarrel after all. To do this you have to figure out whether it is possible to get the amount of gold greater than any preassigned number from some finite amount of sand.

Input: ['100 200 250 150 200 250'] Output:['Ron']

Positive integer number x is called prime, if it has exactly two positive integer divisors. For example, 2, 3, 17, 97 are primes, but 1, 10, 120 are not.You are given an integer number n, find the shortest segment [a, b], which contains n (i.e. a ≤ n ≤ b) and a, b are primes.

Input: ['10'] Output:['7 11']

You are given the prices of three presents. Also there are three sisters. It is known that the most valuable present is for the eldest sister. The second (by price) is for the second sister. And the less valuable present is for the youngest sister. If two (or three) presents have the same price, corresponding sisters may get the in a random way.

Input: ['11 13 1'] Output:['2 1 3 ']

The integer numbers from 1 to nm was put into rectangular table having n rows and m columns. The numbers was put from left to right, from top to bottom, i.e. the first row contains integers 1, 2, ..., m, the second — m + 1, m + 2, ..., 2 * m and so on.After it these numbers was written on the paper in another order: from top to bottom, from left to right. First, the numbers in the first column was written (from top to bottom) and so on.Print the k-th number on the paper.

Input: ['3 4 11'] Output:['8']

The "Bulls and Cows" game needs two people to play. The thinker thinks of a number and the guesser tries to guess it.The thinker thinks of a four-digit number in the decimal system. All the digits in the number are different and the number may have a leading zero. It can't have more than one leading zero, because all it's digits should be different. The guesser tries to guess the number. He makes a series of guesses, trying experimental numbers and receives answers from the first person in the format "x bulls y cows". x represents the number of digits in the experimental number that occupy the same positions as in the sought number. y represents the number of digits of the experimental number that present in the sought number, but occupy different positions. Naturally, the experimental numbers, as well as the sought number, are represented by four-digit numbers where all digits are different and a leading zero can be present.For example, let's suppose that the thinker thought of the number 0123. Then the guessers' experimental number 1263 will receive a reply "1 bull 2 cows" (3 occupies the same positions in both numbers and 1 and 2 are present in both numbers but they occupy different positions). Also, the answer to number 8103 will be "2 bulls 1 cow" (analogically, 1 and 3 occupy the same positions and 0 occupies a different one). When the guesser is answered "4 bulls 0 cows", the game is over.Now the guesser has already made several guesses and wants to know whether his next guess can possibly be the last one.

Input: ['21263 1 28103 2 1'] Output:['Need more data']

Tyndex is again well ahead of the rivals! The reaction to the release of Zoozle Chrome browser was the release of a new browser Tyndex.Brome!The popularity of the new browser is growing daily. And the secret is not even the Tyndex.Bar installed (the Tyndex.Bar automatically fills the glass with the finest 1664 cognac after you buy Tyndex.Bottles and insert in into a USB port). It is highly popular due to the well-thought interaction with the user.Let us take, for example, the system of automatic address correction. Have you entered codehorses instead of codeforces? The gloomy Zoozle Chrome will sadly say that the address does not exist. Tyndex.Brome at the same time will automatically find the closest address and sent you there. That's brilliant!How does this splendid function work? That's simple! For each potential address a function of the F error is calculated by the following rules: for every letter ci from the potential address c the closest position j of the letter ci in the address (s) entered by the user is found. The absolute difference |i - j| of these positions is added to F. So for every i (1 ≤ i ≤ |c|) the position j is chosen such, that ci = sj, and |i - j| is minimal possible. if no such letter ci exists in the address entered by the user, then the length of the potential address |c| is added to F. After the values of the error function have been calculated for all the potential addresses the most suitable one is found. To understand the special features of the above described method better, it is recommended to realize the algorithm of calculating the F function for an address given by the user and some set of potential addresses. Good luck!

Input: ['2 10codeforcescodeforcescodehorses'] Output:['012']

Statistics claims that students sleep no more than three hours a day. But even in the world of their dreams, while they are snoring peacefully, the sense of impending doom is still upon them.A poor student is dreaming that he is sitting the mathematical analysis exam. And he is examined by the most formidable professor of all times, a three times Soviet Union Hero, a Noble Prize laureate in student expulsion, venerable Petr Palych.The poor student couldn't answer a single question. Thus, instead of a large spacious office he is going to apply for a job to thorium mines. But wait a minute! Petr Palych decided to give the student the last chance! Yes, that is possible only in dreams. So the professor began: "Once a Venusian girl and a Marsian boy met on the Earth and decided to take a walk holding hands. But the problem is the girl has al fingers on her left hand and ar fingers on the right one. The boy correspondingly has bl and br fingers. They can only feel comfortable when holding hands, when no pair of the girl's fingers will touch each other. That is, they are comfortable when between any two girl's fingers there is a boy's finger. And in addition, no three fingers of the boy should touch each other. Determine if they can hold hands so that the both were comfortable."The boy any the girl don't care who goes to the left and who goes to the right. The difference is only that if the boy goes to the left of the girl, he will take her left hand with his right one, and if he goes to the right of the girl, then it is vice versa.

Input: ['5 110 5'] Output:['YES']

Valerian was captured by Shapur. The victory was such a great one that Shapur decided to carve a scene of Valerian's defeat on a mountain. So he had to find the best place to make his victory eternal!He decided to visit all n cities of Persia to find the best available mountain, but after the recent war he was too tired and didn't want to traverse a lot. So he wanted to visit each of these n cities at least once with smallest possible traverse. Persian cities are connected with bidirectional roads. You can go from any city to any other one using these roads and there is a unique path between each two cities.All cities are numbered 1 to n. Shapur is currently in the city 1 and he wants to visit all other cities with minimum possible traverse. He can finish his travels in any city.Help Shapur find how much He should travel.

Input: ['31 2 32 3 4'] Output:['7']

It's now 260 AD. Shapur, being extremely smart, became the King of Persia. He is now called Shapur, His majesty King of kings of Iran and Aniran.Recently the Romans declared war on Persia. They dreamed to occupy Armenia. In the recent war, the Romans were badly defeated. Now their senior army general, Philip is captured by Shapur and Shapur is now going to capture Valerian, the Roman emperor.Being defeated, the cowardly Valerian hid in a room at the top of one of his castles. To capture him, Shapur has to open many doors. Fortunately Valerian was too scared to make impenetrable locks for the doors.Each door has 4 parts. The first part is an integer number a. The second part is either an integer number b or some really odd sign which looks like R. The third one is an integer c and the fourth part is empty! As if it was laid for writing something. Being extremely gifted, after opening the first few doors, Shapur found out the secret behind the locks.c is an integer written in base a, to open the door we should write it in base b. The only bad news is that this R is some sort of special numbering system that is used only in Roman empire, so opening the doors is not just a piece of cake!Here's an explanation of this really weird number system that even doesn't have zero:Roman numerals are based on seven symbols: a stroke (identified with the letter I) for a unit, a chevron (identified with the letter V) for a five, a cross-stroke (identified with the letter X) for a ten, a C (identified as an abbreviation of Centum) for a hundred, etc.: I=1 V=5 X=10 L=50 C=100 D=500 M=1000Symbols are iterated to produce multiples of the decimal (1, 10, 100, 1, 000) values, with V, L, D substituted for a multiple of five, and the iteration continuing: I 1, II 2, III 3, V 5, VI 6, VII 7, etc., and the same for other bases: X 10, XX 20, XXX 30, L 50, LXXX 80; CC 200, DCC 700, etc. At the fourth and ninth iteration, a subtractive principle must be employed, with the base placed before the higher base: IV 4, IX 9, XL 40, XC 90, CD 400, CM 900.Also in bases greater than 10 we use A for 10, B for 11, etc.Help Shapur capture Valerian and bring peace back to Persia, especially Armenia.

Input: ['10 21'] Output:['1']

Once upon a time in the thicket of the mushroom forest lived mushroom gnomes. They were famous among their neighbors for their magic mushrooms. Their magic nature made it possible that between every two neighboring mushrooms every minute grew another mushroom with the weight equal to the sum of weights of two neighboring ones. The mushroom gnomes loved it when everything was in order, that's why they always planted the mushrooms in one line in the order of their weights' increasing. Well... The gnomes planted the mushrooms and went to eat. After x minutes they returned and saw that new mushrooms had grown up, so that the increasing order had been violated. The gnomes replanted all the mushrooms in the correct order, that is, they sorted the mushrooms in the order of the weights' increasing. And went to eat again (those gnomes were quite big eaters). What total weights modulo p will the mushrooms have in another y minutes?

Input: ['2 1 0 6572765451 2'] Output:['6']

Misha decided to help Pasha and Akim be friends again. He had a cunning plan — to destroy all the laughy mushrooms. He knows that the laughy mushrooms can easily burst when they laugh. Mushrooms grow on the lawns. There are a[t] mushrooms on the t-th lawn.Misha knows that the lawns where the mushrooms grow have a unique ability. A lawn (say, i) can transfer laugh to other lawn (say, j) if there exists an integer (say, b) such, that some permutation of numbers a[i], a[j] and b is a beautiful triple (i ≠ j). A beautiful triple is such three pairwise coprime numbers x, y, z, which satisfy the following condition: x2 + y2 = z2.Misha wants to know on which minimal number of lawns he should laugh for all the laughy mushrooms to burst.

Input: ['12'] Output:['1']

Pasha and Akim were making a forest map — the lawns were the graph's vertexes and the roads joining the lawns were its edges. They decided to encode the number of laughy mushrooms on every lawn in the following way: on every edge between two lawns they wrote two numbers, the greatest common divisor (GCD) and the least common multiple (LCM) of the number of mushrooms on these lawns. But one day Pasha and Akim had an argument about the laughy mushrooms and tore the map. Pasha was left with just some part of it, containing only m roads. Your task is to help Pasha — use the map he has to restore the number of mushrooms on every lawn. As the result is not necessarily unique, help Pasha to restore any one or report that such arrangement of mushrooms does not exist. It is guaranteed that the numbers on the roads on the initial map were no less that 1 and did not exceed 106.

Input: ['1 0'] Output:['YES1 ']

Recently personal training sessions have finished in the Berland State University Olympiad Programmer Training Centre. By the results of these training sessions teams are composed for the oncoming team contest season. Each team consists of three people. All the students of the Centre possess numbers from 1 to 3n, and all the teams possess numbers from 1 to n. The splitting of students into teams is performed in the following manner: while there are people who are not part of a team, a person with the best total score is chosen among them (the captain of a new team), this person chooses for himself two teammates from those who is left according to his list of priorities. The list of every person's priorities is represented as a permutation from the rest of 3n - 1 students who attend the centre, besides himself.You are given the results of personal training sessions which are a permutation of numbers from 1 to 3n, where the i-th number is the number of student who has won the i-th place. No two students share a place. You are also given the arrangement of the already formed teams in the order in which they has been created. Your task is to determine the list of priorities for the student number k. If there are several priority lists, choose the lexicographically minimal one.

Input: ['35 4 1 2 6 3 7 8 95 6 29 3 41 7 84'] Output:['2 3 5 6 9 1 7 8 ']

BerOilGasDiamondBank has branches in n cities, at that n is an even number. The bank management wants to publish a calendar with the names of all those cities written in two columns: the calendar should consist of exactly n / 2 lines of strictly equal length, each of which contains exactly two names and exactly one separator character between them. The name of every city should be used in the calendar exactly once. For historical reasons the symbol d is used as the separator of words in the calendar. The BerOilGasDiamondBank management wants to show that all its branches are equally important to it, that's why the order of their appearance in the calendar should be following: if we "glue"(concatinate) all the n / 2 calendar lines (from top to bottom) to make a single line, then the lexicographically minimal line is obtained. No separator character will be used to separate calendar lines. For example, if the lines are "bertown!berville", "newberville!bera", then the resulting line is "bertown!bervillenewberville!bera". In some sense one has to find the lexicographically minimal calendar, where the comparison of calendars happens line by line.Help BerOilGasDiamondBank and construct the required calendar.

Input: ['4baahgc.'] Output:['aa.bc.hg']

On Bertown's main street n trees are growing, the tree number i has the height of ai meters (1 ≤ i ≤ n). By the arrival of the President of Berland these trees were decided to be changed so that their heights formed a beautiful sequence. This means that the heights of trees on ends (the 1st one and the n-th one) should be equal to each other, the heights of the 2-nd and the (n - 1)-th tree must also be equal to each other, at that the height of the 2-nd tree should be larger than the height of the first tree by 1, and so on. In other words, the heights of the trees, standing at equal distance from the edge (of one end of the sequence) must be equal to each other, and with the increasing of the distance from the edge by 1 the tree height must also increase by 1. For example, the sequences "2 3 4 5 5 4 3 2" and "1 2 3 2 1" are beautiful, and '1 3 3 1" and "1 2 3 1" are not. Changing the height of a tree is a very expensive operation, using advanced technologies invented by Berland scientists. In one operation you can choose any tree and change its height to any number, either increase or decrease. Note that even after the change the height should remain a positive integer, i. e, it can't be less than or equal to zero. Identify the smallest number of changes of the trees' height needed for the sequence of their heights to become beautiful.

Input: ['32 2 2'] Output:['1']