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 <vector>
#include <utility>
#include <algorithm>
using namespace std;

int main(){
    int n, m;
    cin >> n >> m;
    vector<int> which_set(n, 0);
    vector<vector<pair<int, int>>> sets(n);
    for(int i = 0, p; i < n; ++i){
        cin >> p;
        --p;
        sets[i].emplace_back(i, p);
        which_set[i] = i; }

    for(int i = 0, x, y; i < m; ++i){
        cin >> x >> y;
        --x, --y;
        x = which_set[x];
        y = which_set[y];
        if(sets[x].size() > sets[y].size()) swap(x, y);
        for(auto p : sets[x]){
            which_set[p.first] = y;
            sets[y].push_back(p); }
        sets[x].clear(); }

    int rez = 0;

    for(auto& x : sets){
        vector<int> s1, s2;
        for(auto& y : x)
            s1.push_back(y.first),
            s2.push_back(y.second);

        sort(begin(s1), end(s1));
        sort(begin(s2), end(s2));
        
        vector<int> tmp;
        set_intersection(begin(s1), end(s1),
            begin(s2), end(s2),
            back_inserter(tmp));

        rez += tmp.size(); }

    cout << rez << endl;
    return 0; }