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)

namespace AtCoderCS
{
    using System;
    using System.Collections.Generic;
    using System.IO;
    using System.Text;
    using System.Linq;
    using static System.Console;
    using static System.Math;
    using static Macro;

    class Program
    {
        void Solve()
        {
            var N = IN.Int;
            var M = IN.Int;
            var K = IN.Int;
            var A = new int[M];
            var B = new int[M];
            var C = new int[K];
            var D = new int[K];
            REP(M, i =>
            {
                A[i] = IN.Int - 1;
                B[i] = IN.Int - 1;
            });
            REP(K, i =>
            {
                C[i] = IN.Int - 1;
                D[i] = IN.Int - 1;
            });
            var g = new UnionFind(N);
            var friend = new List<int>[N];
            var block = new List<int>[N];
            REP(N, i =>
            {
                friend[i] = new List<int>();
                block[i] = new List<int>();
            });
            REP(M, i =>
            {
                friend[A[i]].Add(B[i]);
                friend[B[i]].Add(A[i]);
                g.Unite(A[i], B[i]);
            });
            REP(K, i =>
            {
                block[C[i]].Add(D[i]);
                block[D[i]].Add(C[i]);
            });
            var ans = new int[N];
            REP(N, i =>
            {
                ans[i] = g.Size(i) - friend[i].Count() - 1;
                foreach (var x in block[i])
                {
                    if (g.Find(i, x)) ans[i]--;
                }
            });
            WriteLine(string.Join(" ", ans));
        }

        private SimpleInput IN = new SimpleInput();
        private SimpleOutput OUT = new SimpleOutput();

        void Stream()
        {
            Solve();
            OUT.Flush();
        }

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

    #region IO
    class SimpleInput
    {
        private string[] _nextBuffer;
        private int _bufferCnt;
        private readonly char[] _cs = new char[] {' ', '"', ','};

        public SimpleInput()
        {
            _nextBuffer = new string[0];
            _bufferCnt = 0;
        }

        string Next()
        {
            if (_bufferCnt < _nextBuffer.Length) return _nextBuffer[_bufferCnt++];
            var st = ReadLine();
            while (st == string.Empty) st = ReadLine();
            if (st != null) _nextBuffer = st.Split(_cs, StringSplitOptions.RemoveEmptyEntries);
            _bufferCnt = 0;
            return _nextBuffer[_bufferCnt++];
        }

        public string String => Next();
        public char Char => char.Parse(String);
        public int Int => int.Parse(String);
        public long Long => long.Parse(String);
        public double Double => double.Parse(String);
    }

    class SimpleOutput
    {
        private readonly StreamWriter _sw = new StreamWriter(OpenStandardOutput())
        {
#if DEBUG
            AutoFlush = true
#else
            AutoFlush = false
#endif
        };

        public SimpleOutput()
        {
            SetOut(_sw);
        }

        public void Flush() => Out.Flush();
    }
    #endregion

    #region MACRO
    static class Macro
    {
        public static void FOR(int a, int b, int n, Action<int> f)
        {
            for (int i = a; i < b; i += n) f(i);
        }

        public static void FOR(int a, int b, Action<int> f) => FOR(a, b, 1, f);
        public static void REP(int a, Action<int> f) => FOR(0, a, f);
    }
    #endregion

    class UnionFind
    {
        private int[] data;

        public UnionFind(int n)
        {
            data = new int[n + 1];
            for (var i = 0; i < n + 1; ++i) data[i] = -1;
        }

        public void Unite(int x, int y)
        {
            x = Root(x);
            y = Root(y);
            if (x == y) return;
            if (data[y] < data[x]) Swap(ref x, ref y);
            data[x] += data[y];
            data[y] = x;
        }

        public bool Find(int x, int y) => Root(x) == Root(y);
        public int Root(int x) => data[x] < 0 ? x : Root(data[x]);
        public int Size(int x) => -data[Root(x)];

        private void Swap(ref int a, ref int b)
        {
            var tmp = b;
            b = a;
            a = tmp;
        }
    }
}