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: Accepted)

n, m = map(int, input().split())
P = list(map(int, input().split()))
X = [list(map(int, input().split())) for i in range(m)]

for i in range(n):
    P[i] -= 1
for i in range(m):
    for j in range(2):
        X[i][j] -= 1

M = [[] for i in range(n)]

for i in range(m):
    M[X[i][0]].append(X[i][1])
    M[X[i][1]].append(X[i][0])

G = [0] * n
clr = 0

for i in range(n):
    if G[i] == 0 and len(M[i]) > 0:
        clr += 1
        G[i] = clr
        
        Q = M[i][:]
        st = 0
        while st < len(Q):
            if G[Q[st]] == 0:
                G[Q[st]] = clr
                for item in M[Q[st]]:
                    Q.append(item)

            st += 1

# print(G)

ans = 0
for i in range(n):
    if G[i] == 0 and i == P[i]:
        ans += 1

G2 = [[[], []] for i in range(clr+1)]

for i in range(n):
    G2[G[i]][0].append(i)
    G2[G[i]][1].append(P[i])
# print(G2)
# print(ans)

for i in range(1, clr+1):
    ans += len(G2[i][0]) * 2 - len(set(G2[i][0] + G2[i][1]))

print(ans)