We have a tree with N vertices and N-1 edges, respectively numbered 1, 2,\cdots, N and 1, 2, \cdots, N-1. Edge i connects Vertex u_i and v_i.
For integers L, R (1 \leq L \leq R \leq N), let us define a function f(L, R) as follows:
 - Let S be the set of the vertices numbered L through R. f(L, R) represents the number of connected components in the subgraph formed only from the vertex set S and the edges whose endpoints both belong to S.
Compute \sum_{L=1}^{N} \sum_{R=L}^{N} f(L, R).

-----Constraints-----
 - 1 \leq N \leq 2 \times 10^5
 - 1 \leq u_i, v_i \leq N
 - The given graph is a tree.
 - All values in input are integers.

-----Input-----
Input is given from Standard Input in the following format:
N
u_1 v_1
u_2 v_2
:
u_{N-1} v_{N-1}

-----Output-----
Print \sum_{L=1}^{N} \sum_{R=L}^{N} f(L, R).

-----Sample Input-----
3
1 3
2 3

-----Sample Output-----
7

We have six possible pairs (L, R) as follows:
 - For L = 1, R = 1, S = \{1\} and we have 1 connected component.
 - For L = 1, R = 2, S = \{1, 2\} and we have 2 connected components.
 - For L = 1, R = 3, S = \{1, 2, 3\} and we have 1 connected component, since S contains both endpoints of each of the edges 1, 2.
 - For L = 2, R = 2, S = \{2\} and we have 1 connected component.
 - For L = 2, R = 3, S = \{2, 3\} and we have 1 connected component, since S contains both endpoints of Edge 2.
 - For L = 3, R = 3, S = \{3\} and we have 1 connected component.
The sum of these is 7.