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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <cstdio>
#include <climits>
#include <cstdlib>
#include <cmath>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <queue>
#include <deque>
#include <stack>
#include <map>
#include <list>
#include <set>
#include <bitset>
#include <iterator>
#define loop(i, a, b) for(int i = (int)(a); i < (int)(b); i++)
#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define debug(x)  cout << #x << " = " << (x) << endl;

using namespace std;
using LL = long long;
using ULL = unsigned long long;
struct UnionFind {
    vector<int> par;

    UnionFind(int n) {
        par.assign(n, -1);
    }

    int root(int x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }
    bool is_same(int x, int y) {
        return root(x) == root(y);
    }
    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) return false;
        if (par[x] > par[y]) swap(x, y);
        par[x] += par[y];
        par[y] = x;
        return true;
    }
    int size(int x) {
        return -par[root(x)];
    }
};

int main() {
    int n, m; cin >> n >> m;
    vector<int> p(n);
    rep(i, n) {
        cin >> p[i];
        p[i]--;
    }
    UnionFind uf(n);
    rep(i, m) {
        int x, y; cin >> x >> y;
        uf.merge(x, y);
    }
    int ans = 0;
    rep(i, n) {
        if (i == p[i]) {
            ans++;
            continue;
        }

        if (uf.is_same(i, p[i])) ans++;
    }
    cout << ans << endl;
    return 0;
}