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 AtCoderBeginnerContest157.Questions;
using AtCoderBeginnerContest157.Extensions;
using System;
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System.Text;

namespace AtCoderBeginnerContest157.Questions
{
    // 復習
    public class QuestionD_UnionFind : AtCoderQuestionBase
    {
        int n, m, k;
        UnionFindNode<int>[] people = null;
        List<int>[] friends = null;
        int[] blockCount;
        int[] group;
        List<int> groupMemberCount = new List<int>();

        public override IEnumerable<object> Solve(TextReader inputStream)
        {
            var nmk = inputStream.ReadIntArray();
            n = nmk[0];
            m = nmk[1];
            k = nmk[2];

            people = Enumerable.Range(0, n).Select(i => new UnionFindNode<int>(i)).ToArray();
            friends = Enumerable.Range(0, n).Select(_ => new List<int>()).ToArray();
            group = Enumerable.Repeat(-1, n).ToArray();
            blockCount = new int[n];

            for (int i = 0; i < m; i++)
            {
                var ab = inputStream.ReadIntArray();
                var a = ab[0] - 1;
                var b = ab[1] - 1;
                people[a].Unite(people[b]);
                friends[a].Add(b);
                friends[b].Add(a);
            }

            for (int i = 0; i < k; i++)
            {
                var cd = inputStream.ReadIntArray();
                if (people[cd[0] - 1].IsInSameGroup(people[cd[1] - 1]))
                {
                    blockCount[cd[0] - 1] += 1;
                    blockCount[cd[1] - 1] += 1;
                }
            }

            yield return string.Join(" ", Enumerable.Range(0, n).Select(i => GetFriendCount(i).ToString()));
        }

        int GetFriendCount(int me)
        {
            return people[me].GetSize() - friends[me].Count - blockCount[me] - 1;
        }
    }

    public class UnionFindNode<T>
    {
        private int _height;    // rootのときのみ有効
        private int _size;      // 同上
        private UnionFindNode<T> _parent;
        public T Item { get; }

        public UnionFindNode(T item)
        {
            _height = 0;
            _size = 1;
            _parent = this;
            Item = item;
        }

        public UnionFindNode<T> FindRoot()
        {
            if (_parent != this) // not ref equals
            {
                var root = _parent.FindRoot();
                _parent = root;
            }

            return _parent;
        }

        public int GetSize() => FindRoot()._size;

        public void Unite(UnionFindNode<T> other)
        {
            var thisRoot = this.FindRoot();
            var otherRoot = other.FindRoot();
            if (thisRoot._height < otherRoot._height)
            {
                thisRoot._parent = otherRoot;
                thisRoot._size = otherRoot._size;
                otherRoot._height = Math.Max(thisRoot._height + 1, otherRoot._height);
            }
            else
            {
                otherRoot._parent = thisRoot;
                otherRoot._size = thisRoot._size;
                thisRoot._height = Math.Max(otherRoot._height + 1, thisRoot._height);
            }
        }

        public bool IsInSameGroup(UnionFindNode<T> other) => this.FindRoot() == other.FindRoot();
    }
}


namespace AtCoderBeginnerContest157
{
    class Program
    {
        static void Main(string[] args)
        {
            IAtCoderQuestion question = new QuestionD_UnionFind();    // 問題に合わせて書き換え
            var answers = question.Solve(Console.In);
            foreach (var answer in answers)
            {
                Console.WriteLine(answer);
            }
        }
    }
}

#region Base Classes

namespace AtCoderBeginnerContest157.Questions
{

    public interface IAtCoderQuestion
    {
        IEnumerable<object> Solve(string input);
        IEnumerable<object> Solve(TextReader inputStream);
    }

    public abstract class AtCoderQuestionBase : IAtCoderQuestion
    {
        public IEnumerable<object> Solve(string input)
        {
            var stream = new MemoryStream(Encoding.Unicode.GetBytes(input));
            var reader = new StreamReader(stream, Encoding.Unicode);

            return Solve(reader);
        }

        public abstract IEnumerable<object> Solve(TextReader inputStream);
    }

}

#endregion

#region Extensions

namespace AtCoderBeginnerContest157.Extensions
{
    internal static class TextReaderExtensions
    {
        internal static int ReadInt(this TextReader reader) => int.Parse(ReadString(reader));
        internal static long ReadLong(this TextReader reader) => long.Parse(ReadString(reader));
        internal static double ReadDouble(this TextReader reader) => double.Parse(ReadString(reader));
        internal static string ReadString(this TextReader reader) => reader.ReadLine();

        internal static int[] ReadIntArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(int.Parse).ToArray();
        internal static long[] ReadLongArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(long.Parse).ToArray();
        internal static double[] ReadDoubleArray(this TextReader reader, char separator = ' ') => ReadStringArray(reader, separator).Select(double.Parse).ToArray();
        internal static string[] ReadStringArray(this TextReader reader, char separator = ' ') => reader.ReadLine().Split(separator);
    }
}

#endregion