Problem Statement

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 $\sum_{L=1}^{N} \sum_{R=L}^{N} f(L, R)$.

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 $\sum_{L=1}^{N} \sum_{R=L}^{N} f(L, R)$.

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.

Sample Input 1

3
1 3
2 3

Sample Output 1

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.

Sample Input 2

2
1 2

Sample Output 2

3

Sample Input 3

10
5 3
5 7
8 9
1 9
9 10
8 4
7 4
6 10
7 2

Sample Output 3

113

见题面 Input 部分

见题面 Output 部分