B"You're given a tree with n vertices. The color of the i -th vertex is h_{i} . The value of the tree is defined as sum limits_{h_{i} = h_{j}, 1 <= i < j <= n}{dis(i,j)} , where dis(i,j) is the number of edges on the shortest path between i and j . The color of each vertex is lost, you only remember that h_{i} can be any integer from [l_{i}, r_{i}] (inclusive). You want to calculate the sum of values of all trees meeting these conditions modulo 10^9 + 7 (the set of edges is fixed, but each color is unknown, so there are prod limits_{i = 1}^{n} (r_{i} - l_{i} + 1) different trees). The first line contains one integer n ( 2 <= n <= 10^5 ) -- the number of vertices. Then n lines follow, each line contains two integers l_i and r_i ( 1 <= l_i <= r_i <= 10^5 ) denoting the range of possible colors of vertex i . Then n - 1 lines follow, each containing two integers u and v ( 1 <= u, v <= n , u ne v ) denoting an edge of the tree. It is guaranteed that these edges form a tree. Print one integer -- the sum of values of all possible trees, taken modulo 10^9 + 7 . In the first example there are four different ways to color the tree (so, there are four different trees): Overall the sum of all values is 10+4+4+4=22 . "...