100973: [AtCoder]ABC097 D - Equals

Problem Statement

We have a permutation of the integers from $1$ through $N$, $p_1$, $p_2$, .., $p_N$. We also have $M$ pairs of two integers between $1$ and $N$ (inclusive), represented as $(x_1,y_1)$, $(x_2,y_2)$, .., $(x_M,y_M)$. AtCoDeer the deer is going to perform the following operation on $p$ as many times as desired so that the number of $i$ ($1$ $≤$ $i$ $≤$ $N$) such that $p_i = i$ is maximized:

• Choose $j$ such that $1$ $≤$ $j$ $≤$ $M$, and swap $p_{x_j}$ and $p_{y_j}$.

Find the maximum possible number of $i$ such that $p_i = i$ after operations.

Constraints

• $2$ $≤$ $N$ $≤$ $10^5$
• $1$ $≤$ $M$ $≤$ $10^5$
• $p$ is a permutation of integers from $1$ through $N$.
• $1$ $≤$ $x_j,y_j$ $≤$ $N$
• $x_j$ $≠$ $y_j$
• If $i$ $≠$ $j$, $\{x_i,y_i\}$ $≠$ $\{x_j,y_j\}$.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $M$
$p_1$ $p_2$ $..$ $p_N$
$x_1$ $y_1$
$x_2$ $y_2$
$:$
$x_M$ $y_M$

Output

Print the maximum possible number of $i$ such that $p_i = i$ after operations.

Sample Input 1

5 2
5 3 1 4 2
1 3
5 4

Sample Output 1

2

If we perform the operation by choosing $j=1$, $p$ becomes 1 3 5 4 2, which is optimal, so the answer is $2$.

Sample Input 2

3 2
3 2 1
1 2
2 3

Sample Output 2

3

If we perform the operation by, for example, choosing $j=1$, $j=2$, $j=1$ in this order, $p$ becomes 1 2 3, which is obviously optimal. Note that we may choose the same $j$ any number of times.

Sample Input 3

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

Sample Output 3

8

Sample Input 4

5 1
1 2 3 4 5
1 5

Sample Output 4

5

We do not have to perform the operation.