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.Collections.Generic;
using System.Linq;

namespace AtCoderBeginnerContest157
{
	class Program
	{
		static void Main(string[] args)
		{
			var nm = ReadIntArray();
			var pairs = new List<int[]>(nm[1]);
			for(var i = 0; i < nm[1]; i++)
			{
				var tmp = ReadIntArray();
				if ((nm[0] != 1  &&  tmp[0] == 1 && tmp[1] == 0)
					|| (i != 0 && pairs.Any(x => x[0] == tmp[0] && x[1] != tmp[1])))
				{
					Console.WriteLine("-1");
					return;
				}
				pairs.Add(tmp);
			}

			switch (nm[0])
			{
				case 1:
				{
					if(nm[1] != 0 && pairs.Any(x => x[0] == 1))
					{
						Console.WriteLine(pairs.Where(x => x[0] == 1).ToArray()[0][1]);
						return;
					}
					else
					{
						Console.WriteLine(0);
						return;
					}
				}
				case 2:
				{
					var two = 1;
					var one = 0;
					if(nm[1] != 0 && pairs.Any(x => x[0] == 1))
					{
						two = pairs.Where(x => x[0] == 1).ToArray()[0][1];
					}
					if(nm[1] != 0 && pairs.Any(x => x[0] == 2))
					{
						one = pairs.Where(x => x[0] == 2).ToArray()[0][1];
					}
					Console.WriteLine(two * 10 + one);
					return;
				}
				case 3:
				{
					var three = 1;
					var two = 0;
					var one = 0;
					if (nm[1] != 0 && pairs.Any(x => x[0] == 1))
					{
						three = pairs.Where(x => x[0] == 1).ToArray()[0][1];
					}
					if (nm[1] != 0 && pairs.Any(x => x[0] == 2))
					{
						two = pairs.Where(x => x[0] == 2).ToArray()[0][1];
					}
					if (nm[1] != 0 && pairs.Any(x => x[0] == 3))
					{
						one = pairs.Where(x => x[0] == 3).ToArray()[0][1];
					}
					Console.WriteLine(three * 100 + two * 10 + one);
					return;
				}
			}
		}

		public static int ReadInt()
			=> int.Parse(Console.ReadLine());

		public static int[] ReadIntArray()
			=> Console.ReadLine().Split().Select(x => int.Parse(x)).ToArray();

		public static long ReadLong()
			=> long.Parse(Console.ReadLine());

		public static long[] ReadLongArray()
			=> Console.ReadLine().Split().Select(x => long.Parse(x)).ToArray();

		public static string ReadString()
			=> Console.ReadLine();

		public static string[] ReadStringArray()
			=> Console.ReadLine().Split();
	}
}