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: Runtime Error)

#include <iostream>
#include <string>
#include <vector>
#include <unordered_map>
#include <unordered_set>
#include <algorithm>
#include <iterator>
using namespace std;

//using D = unordered_set<int>;
class D : public unordered_set<int>
{
private:
	D* child;
	
public:
	D ()
		: child(nullptr)
	{}

	void joint(D* r)
	{
		child = r;
	}
	
	const_iterator find(int x) const
	{
		auto itr = unordered_set<int>::find(x);
		if (end() == itr)
		{
			if (nullptr != child)
			{
				auto citr = child->find(x);
				if (child->end() != citr) return citr;
				else return end();
			}
			else return end();
		}
		else return itr;
	}
};
int main ()
{
	int n, m;
	cin >> n >> m;

	vector<int> p(n);
	vector<D> rels;
	rels.reserve(n);
	for (int i=0; i<n; ++i)
	{
		cin >> p[i];
		--p[i];
	}

	vector<D *> rels_map;
	rels_map.resize(n, nullptr);
	{
		int x, y;
		for (int i=0; i<m; ++i)
		{
			cin >> x >> y;
			--x;
			--y;
			int s = p[x], t = p[y];

			if (nullptr != rels_map[s])
			{
				if (nullptr != rels_map[t])
				{
					if (rels_map[s] != rels_map[t])
					{
						//rels_map[s]->insert(tmp_map.begin(), tmp_map.end());
						rels_map[s]->joint(rels_map[t]);

						for (auto tx : *rels_map[t]) rels_map[p[tx]] = rels_map[s];
					}
				}
				else
				{
					(rels_map[t] = rels_map[s])->insert(y);
				}
			}
			else if (nullptr != rels_map[t])
			{
				(rels_map[s] = rels_map[t])->insert(x);
			}
			else
			{
				rels.emplace_back();
				auto &back = rels.back();
				(rels_map[s] = &back)->insert(x);
				(rels_map[t] = &back)->insert(y);
			}
		}
	}
	
	int ans = 0;
	for (int i=0; i<n; ++i)
	{
		if (nullptr != rels_map[i])
		{
			if (rels_map[i]->end() != rels_map[i]->find(i))
			{
				++ans;
			}
		}
		else if (i == p[i] /* && nullptr == rels_map[i] */)
		{
			++ans;
		}
	}
	
	cout << ans << endl;
	return 0;
}