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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;
// ReSharper disable PossibleNullReferenceException
// ReSharper disable AssignNullToNotNullAttribute

namespace ProCon
{
    internal class Program
    {
        private static List<int>[] _link;
        private static int[] _group;

        private static void Main(string[] args)
        {
            var nmk = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
            var n = nmk[0];
            var m = nmk[1];
            var k = nmk[2];
            _link = new List<int>[n];
            _group = new int[n];
            var hate = new List<int>[n];
            for (int i = 0; i < n; ++i)
            {
                _link[i] = new List<int>();
                hate[i] = new List<int>();
                _group[i] = -1;
            }

            for (int i = 0; i < m; ++i)
            {
                var ab = Console.ReadLine().Split(' ').Select(tmp=>int.Parse(tmp)-1).ToArray();
                _link[ab[0]].Add(ab[1]);
                _link[ab[1]].Add(ab[0]);
            }
            for (int i = 0; i < k; ++i)
            {
                int[] cd =  Console.ReadLine().Split(' ').Select(tmp=>int.Parse(tmp)-1).ToArray();
                hate[cd[0]].Add(cd[1]);
                hate[cd[1]].Add(cd[0]);
            }

            int groupId = 0;
            int[] groupMemberNum = new int[n];
            for (int i = 0; i < n; ++i)
            {
                if (_group[i] != -1) continue;
                groupMemberNum[groupId] = Visit(i, groupId);
                groupId++;
            }
            var suggest = new int[n];
            for (int i = 0; i < n; ++i)
            {
                var g = _group[i];
                suggest[i] = groupMemberNum[g]-1-_link[i].Count- hate[i].Count(tmp => _group[tmp] == g);
            }
            Console.WriteLine(string.Join(" ", suggest.Select(tmp=>tmp.ToString())));
        }

        private static int Visit(int idx, int group)
        {
            if (_group[idx] != -1) return 0;
            int num = 1;
            _group[idx] = group;
            foreach (var l in _link[idx])
            {
                num+=Visit(l, group);
            }
            return num;
        }
    }
}