Problem:
Score : 400 points

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.

Solution in Python (3.4.3) (judge verdict: Accepted)

import sys

n, m = map(int, sys.stdin.readline().split())
*p, = map(int, sys.stdin.readline().split())
xy = list(zip(*[map(int, sys.stdin.read().split())] * 2))

g = [[] for _ in range(n+1)]
for x, y in xy:
    g[x-1].append(y-1)
    g[y-1].append(x-1)

root = list(range(n))
height = [0] * n

def find_root(v):
    u = root[v]
    if u == v:
        return u
    w = find_root(u)
    root[v] = w
    return w

def unite(v, u):
    rv = find_root(v)
    ru = find_root(u)
    if root[rv] == root[ru]:
        return
    if height[rv] >= height[ru]:
        root[ru] = rv
        height[rv] = max(height[rv], ru+1)
    else:
        root[rv] = ru

def main():
    for x, y in xy:
        unite(x-1, y-1)

    for i in range(n):
        find_root(i)
    
    cnt = 0
    for i in range(n):
        cnt += (root[i] == root[p[i]-1]) & 1
    
    return cnt
    
if __name__ == '__main__':
    ans = main()
    print(ans)