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: Time Limit Exceeded)

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

public class AtCoderD
{
    static void Main()
    {
        int n;
        int m;
        int k;
        {
            var line = Console.ReadLine();
            var words = line.Split(' ');
            n = int.Parse(words[0]);
            m = int.Parse(words[1]);
            k = int.Parse(words[2]);
        }

        List<List<int>> friendGroups = new List<List<int>>();
        List<string> friends = new List<string>();
        for (int i = 0; i < m; i++)
        {
            var line = Console.ReadLine();
            var words = line.Split(' ');
            int a = int.Parse(words[0]);
            int b = int.Parse(words[1]);
            friends.Add(a + ":" + b);

            List<int> groupA = null;
            List<int> groupB = null;
            foreach (List<int> group in friendGroups)
            {
                if (group.Contains(a))
                {
                    groupA = group;
                }
                if (group.Contains(b))
                {
                    groupB = group;
                }
            }
            if (groupA == null && groupB == null)
            {
                List<int> list = new List<int>();
                list.Add(a);
                list.Add(b);
                friendGroups.Add(list);
            }
            else if (groupA == null)
            {
                groupB.Add(a);
            }
            else if (groupB == null)
            {
                groupA.Add(b);
            }
            else if (groupA != groupB)
            {
                groupA.AddRange(groupB);
                groupA = groupA.Distinct().ToList();
                friendGroups.Remove(groupB);
            }
        }

        List<string> blocks = new List<string>();
        for (int i = 0; i < k; i++)
        {
            var line = Console.ReadLine();
            var words = line.Split(' ');
            int a = int.Parse(words[0]);
            int b = int.Parse(words[1]);
            blocks.Add(a + ":" + b);
        }

        string answer = "";
        for (int i = 1; i <= n; i++)
        {
            List<int> targetGroup = null;
            foreach (List<int> group in friendGroups)
            {
                if (group.Contains(i))
                {
                    targetGroup = group;
                    break;
                }
            }

            if (targetGroup == null)
            {
                answer += " " + 0;
                continue;
            }

            int count = 0;
            foreach (int num in targetGroup)
            {
                string str1 = num + ":" + i;
                string str2 = i + ":" + num;
                if (i == num)
                {
                    continue;
                }
                if (friends.Contains(str1) || friends.Contains(str2))
                {
                    continue;
                }
                if (blocks.Contains(str1) || blocks.Contains(str2))
                {
                    continue;
                }
                count++;
            }
            answer += " " + count;

        }

        Console.WriteLine(answer.Trim());
    }
}