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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.util.Scanner;
import java.lang.*;
import java.io.*;
import java.util.*;
import java.lang.Integer;
import java.util.HashMap;

class Main
{
    // driver function to test the above functions
    public static void main(String args[]) throws IOException
    {
        Reader.init(System.in);
        int n = Reader.nextInt();
        int m = Reader.nextInt();
        int k = Reader.nextInt();

        ArrayList<ArrayList<Integer>> list  = new ArrayList<ArrayList<Integer>>();
        ArrayList<ArrayList<Integer>> list2  = new ArrayList<ArrayList<Integer>>();
        int[] ans = new int[n];
        

        for (int i=0; i<n; i++){
            list.add(new ArrayList<Integer>());
            list2.add(new ArrayList<Integer>());
            ans[i]=0;
           
        }

        
        for (int i=0;i<m; i++){
            int val1 = Reader.nextInt();
            int val2 = Reader.nextInt();

            list.get(val1-1).add(val2-1);
            list.get(val2-1).add(val1-1);
        }

        for (int i=0;i<k; i++){
            int val1 = Reader.nextInt();
            int val2 = Reader.nextInt();

            list2.get(val1-1).add(val2-1);
            list2.get(val2-1).add(val1-1);
        }
        solu s = new solu();
        

        for (int i=0; i<n; i++){
            ArrayList<Boolean> b_arr = new ArrayList<Boolean>();
            boolean[] vis = new boolean[n];
            if (vis[i]==false){
                
                s.DFS(i,vis,list,b_arr);
            }
            int count=b_arr.size();
            for (int j=0; j<n; j++){
                if (vis[j]==true){
                    System.out.println(count-1-list.get(j).size()-list2.get(j).size());
                }
            }
            
           
        }
        
    }
    
}

class solu{
    public void DFS(int i, boolean[] vis, ArrayList<ArrayList<Integer>> list, ArrayList<Boolean> b_arr){
        vis[i] = true;
        b_arr.add(true);
        ArrayList<Integer> sub = list.get(i);
        int len = sub.size();
        for (int j=0; j<len; j++){
            int val = sub.get(j);
            if (vis[val]==false){
                DFS(val,vis,list,b_arr);
            }
        }
    }
}

/** Class for buffered reading int and double values */
class Reader {
    static BufferedReader reader;
    static StringTokenizer tokenizer;

    /** call this method to initialize reader for InputStream */
    static void init(InputStream input) {
        reader = new BufferedReader(
                     new InputStreamReader(input) );
        tokenizer = new StringTokenizer("");
    }

    /** get next word */
    static String next() throws IOException {
        while ( ! tokenizer.hasMoreTokens() ) {
            //TODO add check for eof if necessary
            tokenizer = new StringTokenizer(
                   reader.readLine() );
        }
        return tokenizer.nextToken();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt( next() );
    }
    
    static double nextDouble() throws IOException {
        return Double.parseDouble( next() );
    }
}