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: Wrong Answer)



class Board:

    # マス目の数字に島を対応させるdict
    # マージを楽にするため2段になっている
    # m[h[(マス目の数字]] = 島番号
    h = {}
    m = {}

    island = 0  # 現在の島番号

    # hが指す島に新しいマス目を追加する
    def add(self, h, new_item):
        self.h[new_item] = h

    # 2つの島をまとめてひとつにする
    def merge(self, h1, h2):
        self.m[h2] = self.m[h1]

    # 既存の島とつながっていない道が追加されたので新しい島を作って対応させる
    def new_pair(self, x, y):
        new_h = len(self.m) + 1
        self.island += 1

        self.h[x] = new_h
        self.h[y] = new_h
        self.m[new_h] = self.island

    # x, yの間に道を追加する
    def add_pair(self, x, y):
        # x, yが既にある島に含まれるかどうかで場合分け
        if x in self.h:
            h_x = self.h[x]
            if y in self.h:
                h_y = self.h[y]
                if self.m[h_x] == self.m[h_y]:
                    pass
                else:
                    self.merge(h_x, h_y)
            else:
                self.add(h_x, y)
        else:
            if y in self.h:
                self.add(self.h[y], x)
            else:
                self.new_pair(x, y)

    # iからjに移動できるかどうか判定
    def movable(self, i, j):
        return i == j \
               or (i in self.h and j in self.h and self.m[self.h[i]] == self.m[self.h[j]])

    def equals(self, *tips):
        result = 0

        for i, x in enumerate(tips):
            if self.movable(i, x):
                result += 1

        return result


def main():
    n, m = map(int, input().split())
    tips = map(int, input().split())
    board = Board()
    for i in range(m):
        pair = map(int, input().split())
        board.add_pair(*pair)
    print("{0:d}".format(board.equals(*tips)))


main()