Given a rooted tree with $n$ vertices and $m$ pairs $(x_i, y_i)$, where $x_i$ and $y_i$ are vertices of the tree.

For vertices $a$ and $b$ in the tree, define $D(a, b)$ as the number of vertices that are in the subtree rooted at $a$ but not in the subtree rooted at $b$.

You need to find the minimum spanning tree of a complete graph where the vertices are these $m$ pairs, and the weight of the edge between $(x_i, y_i)$ and $(x_j, y_j)$ is $D(x_i, x_j) + D(x_j, x_i) + D(y_i, y_j) + D(y_j, y_i)$.

Input

The first line contains two integers $n$ and $m$.

The next line contains $n-1$ integers, where the $i$-th integer represents the parent $f_{i+1}$ of node $i+1$. It is guaranteed that $f_{i+1} < i+1$.

The next $m$ lines each contain two integers $x_i$ and $y_i$, representing a given pair.

Output

Output a single integer representing the sum of the edge weights of the minimum spanning tree.

Examples

Input 1

5 4
1 2 3 3
3 5
2 2
5 2
2 5

Output 1

7

Note 1

The minimum spanning tree contains edges $(1, 4, 1), (2, 3, 3), (2, 4, 3)$, where the triplet represents the index of the first pair, the index of the second pair, and the edge weight. The sum of the edge weights is $7$.

Subtasks

For $10\%$ of the data, $1 \le n, m \le 1000$.

For another $10\%$ of the data, $1 \le m \le 2 \times 10^4$.

For another $10\%$ of the data, $1 \le m \le 5 \times 10^4$.

For another $20\%$ of the data, $m = n^2$, and all pairs are distinct.

For another $10\%$ of the data, $f_i = i-1$ for all $i = 2, \dots, n$.

For another $10\%$ of the data, $f_i = 1$ for all $i = 2, \dots, n$.

For $100\%$ of the data, $1 \le n \le 10^6, 1 \le m \le 10^5$. For all $i = 1, 2, \dots, n-1$, $1 \le f_{i+1} < i+1$. For all $i = 1, 2, \dots, m$, $1 \le x_i, y_i \le n$.