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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define CHOR 100001

int arr[CHOR];
int sze[CHOR];
 
class dsu
{
	public: int root(int x)
			{
				while(x != arr[x])
				x = arr[arr[x]];
				return x;	
			}
 
			void find_union(int x, int y)
			{
				int rx = root(x);
				int ry = root(y);
				if(rx == ry)
				return;
				if(sze[rx] > sze[ry])
				{
					arr[ry] = rx;
					sze[rx] += sze[ry];
				}	
				else
				{
					arr[rx] = ry;
					sze[ry] += sze[rx];
				}	
				return;
			}
};

int main(void)
{
	int n,m;
	std::cin>>n>>m;
	for(int i=1;i<CHOR;i++)
	{
		arr[i] = i;
		sze[i] = 1;
	}	
	int a[n];
	for(int i=0;i<n;i++)
	std::cin>>a[i];
	dsu T;
	for(int i=0;i<m;i++)
	{
		int x,y;
		std::cin>>x>>y;
		T.find_union(a[x-1], a[y-1]);
	}	
	int ctr = 0;
	for(int i=1;i<=n;i++)
	{
		if(T.root(i) == T.root(a[i-1]))
		ctr++;	
	}	
	std::cout<<ctr<<"\n";
	return 0;	
}