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: Accepted)

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

# use union find

# array and variables are all 0 indexed
class UnionFind
	def initialize(n)
		@parent = Array.new(n){|i| i}
		@rank = Array.new(n){1}
	end
	def find(x)
		par = @parent[x]
		if(par == x)
			return x
		else
			return @parent[x] = find(par)
		end
	end
	def union(x,y)
		root_x = find(x)
		root_y = find(y)
		if(root_x == root_y)
			#ok
			return
		end
		if(@rank[root_x] < @rank[root_y])
			@parent[root_x] = root_y
		elsif(@rank[root_x] == @rank[root_y])
			@parent[root_y] = root_x
			@rank[root_x] += 1
		else
			@parent[root_y] = root_x
		end
	end
	def same_root?(x,y)
		return find(x)==find(y)
	end
end

N,M=gets.chomp.split(' ').map{|n| n.to_i}
P=gets.chomp.split(' ').map{|n| n.to_i - 1}
dpp P

G=UnionFind.new(N)
0.upto(M-1){|d|
	tmp = gets.chomp.split(' ').map{|n| n.to_i - 1}
	G.union(tmp[0],tmp[1])
}

sum = 0
0.upto(N-1){|i|
	if(G.same_root?(i,P[i]))
		sum += 1
	end
}
puts sum