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 C# (Mono 4.6.2.0) (judge verdict: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int[] bk = new int[N];
		int[] fr = new int[N];
		var UF = new UnionFind(N);
		for(int i=0;i<M;i++){
			UF.Unite(A[i], B[i]);
			fr[A[i]]++;
			fr[B[i]]++;
		}
		
		for(int i=0;i<K;i++){
			if(UF.United(C[i], D[i])){
				bk[C[i]]++;
				bk[D[i]]++;
			}
		}
		
		int[] ans = new int[N];
		for(int i=0;i<N;i++){
			int tot = UF.MemCnt(i);
			tot -= fr[i];
			tot -= bk[i];
			ans[i] = tot - 1;
		}
		
		Console.WriteLine(String.Join(" ",ans));
		
		
		
	}
	int N, M, K;
	int[] A,B;
	int[] C,D;
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1]; K = d[2];
		A = new int[M];
		B = new int[M];
		for(int i=0;i<M;i++){
			d = ria();
			A[i] = d[0] - 1;
			B[i] = d[1] - 1; 
		}
		C = new int[K];
		D = new int[K];
		for(int i=0;i<K;i++){
			d = ria();
			C[i] = d[0] - 1;
			D[i] = d[1] - 1;
		}
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}

class UnionFind{
	
	int[] parent;
	int[] mem;
	int compo;
	int N;
	public UnionFind(int n_){
		N = n_;
		parent = new int[N];
		mem = new int[N];
		for(int i = 0; i < N; i++){
			parent[i] = i;
			mem[i] = 1;
		}
		compo = N;
	}
	
	public int Parent(int a){
		if(parent[a] == a) return a;
		return parent[a] = Parent(parent[a]);
	}
	
	public bool United(int a, int b){
		return Parent(a) == Parent(b);
	}
	
	public bool Unite(int a, int b){
		a = Parent(a); b = Parent(b);
		if(a == b) return false;
		if(mem[a] > mem[b]){var t = a; a = b; b = t;}
		parent[a] = b;
		mem[b] += mem[a];
		compo -= 1;
		return true;
	}
	
	public bool IsRoot(int x){
		return x == parent[x];
	}
	public int MemCnt(int x){
		return mem[Parent(x)];
	}
	
	public void Dump(){
		Console.WriteLine(String.Join(" ", parent));
	}
	
	public int Compo{
		get{
			return compo;
		}
	}
	
}