Problem:
Score : 400 points

Problem Statement

An SNS has N users - User 1, User 2, \cdots, User N.

Between these N users, there are some relationships - M friendships and K blockships.

For each i = 1, 2, \cdots, M, there is a bidirectional friendship between User A_i and User B_i.

For each i = 1, 2, \cdots, K, there is a bidirectional blockship between User C_i and User D_i.

We define User a to be a friend candidate for User b when all of the following four conditions are satisfied:

a \neq b.

There is not a friendship between User a and User b.

There is not a blockship between User a and User b.

There exists a sequence c_0, c_1, c_2, \cdots, c_L consisting of integers between 1 and N (inclusive) such that c_0 = a, c_L = b, and there is a friendship between User c_i and c_{i+1} for each i = 0, 1, \cdots, L - 1.

For each user i = 1, 2, ... N, how many friend candidates does it have?

Constraints

All values in input are integers.

2 ≤ N ≤ 10^5

0 \leq M \leq 10^5

0 \leq K \leq 10^5

1 \leq A_i, B_i \leq N

A_i \neq B_i

1 \leq C_i, D_i \leq N

C_i \neq D_i

(A_i, B_i) \neq (A_j, B_j) (i \neq j)

(A_i, B_i) \neq (B_j, A_j)

(C_i, D_i) \neq (C_j, D_j) (i \neq j)

(C_i, D_i) \neq (D_j, C_j)

(A_i, B_i) \neq (C_j, D_j)

(A_i, B_i) \neq (D_j, C_j)

Input

Input is given from Standard Input in the following format:

N M K
A_1 B_1
\vdots
A_M B_M
C_1 D_1
\vdots
C_K D_K

Output

Print the answers in order, with space in between.

Sample Input 1

4 4 1
2 1
1 3
3 2
3 4
4 1

Sample Output 1

0 1 0 1

There is a friendship between User 2 and 3, and between 3 and 4. Also, there is no friendship or blockship between User 2 and 4. Thus, User 4 is a friend candidate for User 2.

However, neither User 1 or 3 is a friend candidate for User 2, so User 2 has one friend candidate.

Sample Input 2

5 10 0
1 2
1 3
1 4
1 5
3 2
2 4
2 5
4 3
5 3
4 5

Sample Output 2

0 0 0 0 0

Everyone is a friend of everyone else and has no friend candidate.

Sample Input 3

10 9 3
10 1
6 7
8 2
2 5
8 4
7 3
10 9
6 4
5 8
2 6
7 5
3 1

Sample Output 3

1 3 5 4 3 3 3 3 1 0

Solution in Julia (0.5.0) (judge verdict: Time Limit Exceeded)

type UF
	n::Int
	pr::Array{Int}
	sz::Array{Int}
	UF(n)=new(n,1:n,ones(Int,n))
end
function find(uf::UF,a::Int)
	if uf.pr[a]==a
		a
	else
		uf.pr[a]=find(uf,uf.pr[a])
	end
end
same(uf::UF,a::Int,b::Int)=find(uf,a)==find(uf,b)
function unite(uf::UF,a::Int,b::Int)
	ap=find(uf,a)
	bp=find(uf,b)
	if ap==bp
		false
	else
		if uf.sz[ap]<uf.sz[bp]
			uf.pr[ap]=bp
			uf.sz[bp]+=uf.sz[ap]
		else
			uf.pr[bp]=ap
			uf.sz[ap]+=uf.sz[bp]
		end
		true
	end
end
size(uf::UF,a::Int)=uf.sz[find(uf,a)]
function main()
	N,M,K=map(x->parse(Int,x),split(readline()))
	uf=UF(N)
	G=[Int[] for _=1:N]
	for _=1:M
		a,b=map(x->parse(Int,x),split(readline()))
		push!(G[a],b)
		push!(G[b],a)
		unite(uf,a,b)
	end
	for _=1:K
		a,b=map(x->parse(Int,x),split(readline()))
		push!(G[a],b)
		push!(G[b],a)
	end
	for i=1:N
		ans=size(uf,i)
		for v=G[i]
			if same(uf,i,v)
				ans-=1
			end
		end
		println(ans-1)
	end
end
main()