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()))

Swap=["" for i in range(M)]

for i in range(M):
    Swap[i]=set(map(int,input().split()))


Y=[set() for i in range(N)]
Unstacked=list(range(M))

Y[0]=Y[0]|Swap[0]
Unstacked.remove(0)
j=0
k=0

while Unstacked!=[]:
    while j <len(Unstacked):

        if Y[k] & Swap[Unstacked[j]] !=set():

            Y[k]=Y[k]|Swap[Unstacked[j]]
            Unstacked.remove(Unstacked[j])
            #print(Y,j,Unstacked)
            j=0

        else:
            j+=1

    if Unstacked!=[]:
        
        k+=1
        Y[k]=Swap[Unstacked[0]]
        Unstacked.remove(Unstacked[0])


#print(Y,j,k,Unstacked)
k+=1
Y[k]=set(range(1,N+1))
for l in range(k):
    Y[k]=Y[k] - Y[l]

count=0

for i in range(k+1):
    for j in list(Y[i]):
        if P[j-1] in Y[i]:
            #print(i,j,P[j-1],Y[i])
            count+=1
        

print(count)