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: Accepted)

using System;
using System.Collections.Generic;
using CompLib.Util;

public class Program
{
    public void Solve()
    {
        var sc = new Scanner();
        int n = sc.NextInt();
        int m = sc.NextInt();
        int k = sc.NextInt();

        var qf = new QuickFind(n);

        int[] friend = new int[n];

        for (int i = 0; i < m; i++)
        {
            int a = sc.NextInt() - 1;
            int b = sc.NextInt() - 1;
            friend[a]++;
            friend[b]++;
            qf.Unite(a, b);
        }

        int[] ans = new int[n];
        for (int i = 0; i < n; i++)
        {
            ans[i] = qf.GetSize(i) - 1 - friend[i];
        }

        for (int i = 0; i < k; i++)
        {
            int c = sc.NextInt() - 1;
            int d = sc.NextInt() - 1;
            if (qf.Same(c, d))
            {
                ans[c]--;
                ans[d]--;
            }
        }

        Console.WriteLine(string.Join(" ", ans));
    }

    public static void Main(string[] args) => new Program().Solve();
}

class QuickFind
{
    // iがいるグループの代表値 _num[i]
    private readonly int[] _num;

    // グループiにある値 
    private readonly List<int>[] _group;

    public QuickFind(int v)
    {
        _num = new int[v];
        _group = new List<int>[v];
        for (int i = 0; i < v; i++)
        {
            _num[i] = i;
            _group[i] = new List<int>();
            _group[i].Add(i);
        }
    }

    public bool Same(int a, int b) => _num[a] == _num[b];

    public bool Unite(int a, int b)
    {
        int numA = _num[a];
        int numB = _num[b];
        if (numA == numB) return false;

        if (_group[numA].Count > _group[numB].Count)
        {
            foreach (int i in _group[numB])
            {
                _group[numA].Add(i);
                _num[i] = numA;
            }
        }
        else
        {
            foreach (int i in _group[numA])
            {
                _group[numB].Add(i);
                _num[i] = numB;
            }
        }

        return true;
    }

    public int GetSize(int i) => _group[_num[i]].Count;
}

namespace CompLib.Util
{
    using System;
    using System.Linq;

    class Scanner
    {
        private string[] _line;
        private int _index;
        private const char Separator = ' ';

        public Scanner()
        {
            _line = new string[0];
            _index = 0;
        }

        public string Next()
        {
            while (_index >= _line.Length)
            {
                _line = Console.ReadLine().Split(Separator);
                _index = 0;
            }

            return _line[_index++];
        }

        public int NextInt() => int.Parse(Next());
        public long NextLong() => long.Parse(Next());
        public double NextDouble() => double.Parse(Next());
        public decimal NextDecimal() => decimal.Parse(Next());
        public char NextChar() => Next()[0];
        public char[] NextCharArray() => Next().ToCharArray();

        public string[] Array()
        {
            _line = Console.ReadLine().Split(' ');
            _index = _line.Length;
            return _line;
        }

        public int[] IntArray() => Array().Select(int.Parse).ToArray();
        public long[] LongArray() => Array().Select(long.Parse).ToArray();
        public double[] DoubleArray() => Array().Select(double.Parse).ToArray();
        public decimal[] DecimalArray() => Array().Select(decimal.Parse).ToArray();
    }
}