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 UnionFind:
    def __init__(self,size):
        self.L = [{'parent':i,'rank':0} for i in range(size)]

    def find(self,x):
        if self.L[x]['parent'] != x:
            self.L[x]['parent'] = self.find(self.L[x]['parent'])
        return self.L[x]['parent']

    def union(self,x,y):
        x_root = self.find(x)
        y_root = self.find(y)
        if x_root == y_root:
            return
        if self.L[x_root]['rank'] < self.L[y_root]['rank']:
            x_root,y_root = y_root,x_root

        self.L[y_root]['parent'] = x_root
        if self.L[x_root]['rank'] == self.L[y_root]['rank']:
            self.L[x_root]['rank'] += 1
    
    def __str__(self):
        return str([i['parent'] for i in self.L])

if __name__ == '__main__':
    N,M = map(int,input().split())
    P = list(map(int,input().split()))
    graph = UnionFind(N)
    for i in [None]*M:
        x,y = map(int,input().split())
        graph.union(x-1,y-1)
    count = 0
    for i,v in enumerate(P):
        if graph.find(i) == graph.find(v-1):
            count += 1
    print(count)