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 PyPy3 (2.4.0) (judge verdict: Time Limit Exceeded)

import sys
 
n, m = [int(i) for i in input().split(" ")]
p = [0] + [int(i) for i in input().split(" ")]
par = [i for i in range(0, n + 1)]
id_set = [{i} for i in range(0, n + 1)]
p_set = [{p[i]} for i in range(0, n + 1)]

sys.setrecursionlimit(10**6)
 
def root(x):
    if par[x] == x:
        return x
    else:
        r = root(par[x])
        par[x] = r
        return r

def unite(x, y):
    x = root(x)
    y = root(y)
    if x == y:
        return
    else:
        par[x] = y
        id_set[y] = id_set[x] | id_set[y]
        p_set[y] = p_set[x] | p_set[y]

for i in range(0, m):
    x, y = [int(i) for i in input().split(" ")]
    unite(x, y)
    
s = 0
for i in range(1, n + 1):
    if i == root(i):
        s += len(id_set[i] & p_set[i])

print(s)