There are lots of things to do on this contest besides this problem, so let's make it quick.
You are given a tree consisting of n vertices. Length of each edge is a real number chosen independently and uniformly at random between 0 and 1. Find the expected value of the diameter of such tree.
The first line of input contains the only integer n (2 ≤ n ≤ 100), the number of vertices in the tree.
Each of the next n - 1 lines contains two integers ui, vi (1 ≤ ui, vi ≤ n, ui ≠ vi) describing endpoints of i-th edge.
Output the answer as a value of a rational number modulo 109 + 7.
Formally, it is guaranteed that under given constraints the expected value of diameter of such random tree is always a rational number 
(p and q are integer and coprime, q is positive), such that q is not divisible by 109 + 7, which is a prime number (in case somebody missed it).
Output such integer a between 0 and 109 + 6 that p - aq is divisible by 109 + 7.
5
1 2
2 3
3 4
4 5
2
5
4 2
2 3
3 1
3 5
283333337
In the first sample case answer is 2 since each edge always belongs to the diameter adding 0.5 to diameter expected length.
In the second sample case expected length of diameter is 
that corresponds to value of a = 283333337 (since 101 - 60·283333337 = - 17000000119 is divisible by 109 + 7).
