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 PyPy3 (2.4.0) (judge verdict: Accepted)

n,m = map(int,input().split())
P = list(map(int,input().split()))
uf = {i:-1 for i in range(1,n+1)}

def get_p(i):
  while uf[i] != i:
    if uf[i] == -1:
      return i
    i = uf[i]
  return i

for _ in range(m):
  x,y = map(int,input().split())
  if x > y:
    x,y = y,x
  if uf[x]== uf[y] == -1:
    uf[x] = x
    uf[y] = x
  elif uf[x] != -1 and uf[y] != -1:
    p = get_p(x)
    uf[x] = p
    index = y
    while index != uf[index]:
      index = uf[y]
      uf[y] = p
      y = index
    else:
      uf[index] = p
  else:
    if uf[x] == -1:
      p = get_p(y)
    else:
      p = get_p(x)
    uf[x] = p
    uf[y] = p

ans = 0  
for i, p in enumerate(P):
  if get_p(i+1) == get_p(p):
    ans += 1
print(ans)