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)

class uf():
    def __init__(self,n):
        self.root = [-1] * (n+1)

    def findroot(self,x):
        if self.root[x] < 0:
            return x
        else:
            self.root[x] = self.findroot(self.root[x])
            return self.root[x]

    def unite(self,x,y):
        rootx = self.findroot(x)
        rooty = self.findroot(y)
        if rootx == rooty:
            return
        else:
            self.root[rootx] += self.root[rooty]
            self.root[rooty] = rootx
            return

    def is_same_group(self,x,y):
        return self.findroot(x) == self.findroot(y)

N,M = map(int, input().split())
P = list(map(int, input().split()))

uf = uf(N)

for _ in range(M):
    x,y = map(int, input().split())
    uf.unite(x,y)

count = 0
for n in range(N):
    if uf.is_same_group(P[n],n+1):
        count += 1

print(count)