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)

import sys

sys.setrecursionlimit(2000000000)


class Node:
    def __init__(self, index):
        self.index = index
        self.neighbors = set()

    def __repr__(self):
        return '{}: {}'.format(self.index, self.neighbors)


def can_go_to_dst(nodes, src_index, dst_index, past_indices):
    if nodes[src_index] is None:
        return False

    neighbor_indices = nodes[src_index].neighbors - past_indices
    if dst_index in neighbor_indices:
        return True

    return any(
        [can_go_to_dst(nodes, ni, dst_index, past_indices | {src_index})] for ni
        in neighbor_indices)


# line_index = 0
#
# def input():
#     global line_index
#     lines = ['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']
#
#     line = lines[line_index]
#     line_index += 1
#     return line


if __name__ == '__main__':
    N, M = map(int, input().split())

    p = []
    desirable_swaps = []
    for i, s in enumerate(input().split()):
        s_value = int(s) - 1
        if i != s_value:
            desirable_swaps.append((s_value, i))

    nodes = [None] * N
    for _ in range(M):
        xy_str = input().split()
        x, y = int(xy_str[0]) - 1, int(xy_str[1]) - 1
        if nodes[x] is None:
            nodes[x] = Node(x)
        if nodes[y] is None:
            nodes[y] = Node(y)

        nodes[x].neighbors |= {y}
        nodes[y].neighbors |= {x}

    first_n_equals = N - len(desirable_swaps)

    n_op_equals = 0
    for src_index, dst_index in desirable_swaps:
        if can_go_to_dst(nodes, src_index, dst_index, set()):
            n_op_equals += 1

    answer = first_n_equals + n_op_equals
    if answer % 2 == 1:
        answer -= 1
    print(answer)
    # print(desirable_swaps)
    # print(nodes)