As the owner of a vast collection of fine ladders, you would like to display them to potential onlookers. You've decided to stand your N ladders up vertically, with their bases at distinct points on a horizontal number line. The ith ladder's base is at position Xi, and it has height Hi.
The local snake population has taken an interest in your ladders. As everyone knows, snakes love nothing more than to suspend themselves horizontally above the ground! In particular, a snake of length L is able to suspend itself between the tops of two ladders a and b if and only if they meet the following conditions:
A number of snakes are planning to take up residence amongst your ladders. In particular, for every position in which a snake could suspend itself (in other words, for every distinct, unordered pair of ladders a and b), one snake will move in of the appropriate length.
You'll have no choice but to take care of these snakes, of course. To feed a snake of length L, it'll cost you L2 dollars daily. To prepare your budget, you'd like to calculate how many dollars you'll be spending each day on your new pets!
Input begins with an integer T, the number of sets of ladders you own. For each set, there is first a line containing the integer N. Then, N lines follow, the ith of which contains two space-separated integers, Xi and Hi.
For the ith set of ladders, print a line containing "Case #i: " followed by the daily feeding cost of all the snakes that move in, modulo 109 + 7.
1 ≤ T ≤ 50
1 ≤ N ≤ 200,000
0 ≤ Xi, Hi ≤ 1,000,000,000
In the first case, one snake will move in between your two ladders. It will have length 20, so it will cost 202 = 400 dollars a day to feed. In the third case, one snake will move in between the ladders of height 3, and another will move in between the ladders at X = 2 and X = 3. The first snake has length 3, and the second has length 1. The total cost is therefore 32 + 12 = 10.