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 (2.7.6) (judge verdict: Time Limit Exceeded)

N,M=map(int,raw_input().split(' '))
p=map(int,raw_input().split(' '))

gr=[]
for _ in range(M):
  x,y=map(int,raw_input().split(' '))
  if len(gr)==0:
    gr.append(set([x,y]))
  else:
    flg=1
    for i in range(len(gr)):
      if x in gr[i] or y in gr[i]:
        gr[i]=gr[i]|set([x,y])
        flg=0
    if flg:
      gr.append(set([x,y]))

def check(g):
  for i in range(len(g)):
    for j in range(i+1,len(g)):
      if len(g[i]&g[j])>0:
        return 0
  return 1

while not check(gr):
  flg=1
  i=0
  while flg:
    for j in range(i+1,len(gr)):
      if len(gr[i]&gr[j])>0:
        gr[i]=gr[i]|gr[j]
        del gr[j]
        flg=0
        break

r_=0
for i in range(len(p)):
  if i==p[i]-1:
    r_+=1

r=0
for g in gr:
  s=set()
  for n in g:
    s.add(p[n-1])
  r += len(g&s)

print max(r,r_)