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: Wrong Answer)

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

class Program
{
    static void Main(string[] args) {
#if DEBUG
        MyDebugger.Test(process, "../TextFile1.txt");
        //MyDebugger.Test(process, "../TextFile2.txt");
        //MyDebugger.MakeTestCase("../TextFile2.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    //static long mod = 1000000007;
    static HashSet<int>[] friends;
    static HashSet<int>[] blocks;
    static HashSet<int>[] friends2;

    static object process(TextReader input) {
        var spl   = input.ReadLine().Split(' ');
        var n     = int.Parse(spl[0]);
        var m     = int.Parse(spl[1]);
        var k     = int.Parse(spl[2]);

        friends  = new HashSet<int>[n];
        blocks   = new HashSet<int>[n];
        friends2 = new HashSet<int>[n];

        for(int i=0; i<n; i++) {
            friends[i]  = new HashSet<int>();
            blocks[i]   = new HashSet<int>();
            //friends2[i] = new HashSet<int>();
        }

        for(int i=0; i<m; i++) {
            spl   = input.ReadLine().Split(' ');
            var a = int.Parse(spl[0]) -1;
            var b = int.Parse(spl[1]) -1;
            friends[a].Add(b);
            friends[b].Add(a);
        }

        for(int i=0; i<k; i++) {
            spl   = input.ReadLine().Split(' ');
            var a = int.Parse(spl[0]);
            var b = int.Parse(spl[1]);
            blocks[a - 1].Add(b - 1);
            blocks[b - 1].Add(a - 1);
        }
        
        for(int i=0; i<n; i++) {
            var net = NetWork(i, new HashSet<int>());
            friends2[i] = net;

            int count = 0;
            //foreach(var x in net) {
            //    if (!friends[i].Contains(x) && !blocks[i].Contains(x) && x != i)
            //        count++;
            //}
#if DEBUG
            Debug.Write(count.ToString());
            Debug.Write(' ');
#else
            Console.Write(count.ToString());
            Console.Write(' ');
#endif
        }

        return null;
    }

    private static HashSet<int> NetWork(int a, HashSet<int> route) {
        var net = new HashSet<int>();

        route.Add(a);

        foreach(var x in friends[a]) {
            if (!net.Contains(x)) net.Add(x);

            if (route.Contains(x)) continue;

            HashSet<int> y;
            if(friends2[x] != null) {
                y = friends2[x];
            } else {
                y = NetWork(x, route);
            }

            foreach (var z in y) {
                if (!net.Contains(z)) net.Add(z);
            }
        }

        return net;
    }
}