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: Accepted)

#union-find-tree
def init(n):
    lis = []
    for i in range(n+1):
        lis.append(i)
    return lis
def find(lis, x):
    if lis[x] == x:
        return x
    else:
        lis[x] = find(lis, lis[x])
        return lis[x]
def sameset(lis, x, y):
    return find(lis, x) == find(lis, y)
def union(lis, x, y):
    x = find(lis, x)
    y = find(lis, y)
    if x != y:
        lis[x] = y

N, M = map(int, input().split())
input_lis = [0]+[int(p) for p in input().split()]
union_find_lis = init(N)
for _ in range(M):
    x, y = map(int, input().split())
    union(union_find_lis, x, y)
count = 0
init_flag = True
for index, num in enumerate(input_lis):
    if init_flag:
        init_flag = False
    else:
        if sameset(union_find_lis, index, num):
            count += 1
print(count)