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)

N,M=map(int,input().split())
p=list(map(int,input().split()))

parent=[i for i in range(N)]
depth=[0 for i in range(N)]
def root(x):
  temp=x
  if parent[x]!=x:
    x=parent[x]
  parent[temp]=x
  return parent[x]

def same(x,y):
  return root(x)==root(y)

def union(x,y):
  x=root(x)
  y=root(y)
  if x==y:
    return
  if depth[x]>depth[y]:
    parent[y]=x
  else:
    parent[x]=y
    if depth[x]==depth[y]:
      depth[x]+=1
  
for i in range(M):
  x,y=map(int,input().split())
  union(x-1,y-1)

roots_nums={}
roots_inds={}
for i in range(N):
  r=root(i)
  if r not in roots_nums:
    roots_nums[r]=[p[i]-1]
    roots_inds[r]=[i]
  else:
    roots_nums[r].append(p[i]-1)
    roots_inds[r].append(i)
    
ans=0
for k in roots_nums.keys():
  ans+=len(set(roots_nums[k])&set(roots_inds[k]))
  
print(ans)