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 Ruby (2.3.3) (judge verdict: Time Limit Exceeded)

require 'pp'
# IS_DEBUG = true
IS_DEBUG = false
def dputs str
	if(IS_DEBUG)
		puts str
	end
end
def dpp str
	if(IS_DEBUG)
		pp str
	end
end

require 'pp'

INT_MAX = 999999999999999999999999

N,M=gets.chomp.split(' ').map{|n| n.to_i}
P=[nil] + gets.chomp.split(' ').map{|n| n.to_i}
dpp P
X = Array.new(M)
0.upto(M-1){|d|
	X[d]=gets.chomp.split(' ').map{|n| n.to_i}
}

S = []

def s_index(n,s)
	s.each_with_index{|set,i|
		if(set.include?(n))
			return i
		end
	}
	return nil
end

# index
def s_merge(n,m,s)
	s[n] = s[n] + s[m]
	s.delete_at(m)
end

def s_add(n,s)
	s << [n]
	return s.size-1
end

X.each{|x,y|
	dpp S
	sx_index = s_index(x,S)
	dputs "sx_index is #{sx_index}"
	if(sx_index.nil?)
		sx_index = s_add(x,S)
	else
		# ok
	end
	sy_index = s_index(y,S)
	if(sy_index.nil?)
		sy_index = sx_index
		S[sx_index] << y
	else
		if(sx_index == sy_index)
			# ok
		else
			s_merge(sx_index,sy_index,S)
		end
	end
}

dpp S
sum = 0
S.each{|set|
	setp = {}
	set.each{|i| 
		setp[P[i]] = P[i]
	}
	dputs "set, setp is"
	dpp set
	dpp setp
	set.each{|i|
		if(! setp[i].nil?)
			sum += 1
		end
	}
}
(Array.new(N+1){|i|i} - S.flatten).each{|i|
	dputs "check #{i}"
	if(P[i] == i)
		dputs "hit "
		sum += 1
	end
}

puts sum