Problem:
Score : 400 points

Problem Statement

We have an H-by-W matrix.
Let a_{ij} be the element at the i-th row from the top and j-th column from the left.
In this matrix, each a_{ij} is a lowercase English letter.

Snuke is creating another H-by-W matrix, A', by freely rearranging the elements in A.
Here, he wants to satisfy the following condition:

Every row and column in A' can be read as a palindrome.

Determine whether he can create a matrix satisfying the condition.

Note

A palindrome is a string that reads the same forward and backward.
For example, a, aa, abba and abcba are all palindromes, while ab, abab and abcda are not.

Constraints

1 ≤ H, W ≤ 100

a_{ij} is a lowercase English letter.

Input

Input is given from Standard Input in the following format:

H W
a_{11}a_{12}...a_{1W}
:
a_{H1}a_{H2}...a_{HW}

Output

If Snuke can create a matrix satisfying the condition, print Yes; otherwise, print No.

Sample Input 1

3 4
aabb
aabb
aacc

Sample Output 1

Yes

For example, the following matrix satisfies the condition.

abba
acca
abba

Sample Input 2

2 2
aa
bb

Sample Output 2

No

It is not possible to create a matrix satisfying the condition, no matter how we rearrange the elements in A.

Sample Input 3

5 1
t
w
e
e
t

Sample Output 3

Yes

For example, the following matrix satisfies the condition.

t
e
w
e
t

Sample Input 4

2 5
abxba
abyba

Sample Output 4

No

Sample Input 5

1 1
z

Sample Output 5

Yes

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.IO;
using System.Linq;
using System.Collections.Generic;
using System.Text;

public class Program
{

	public void Proc()
	{
        int[] inpt = Reader.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
        this.RowCount = inpt[0];
        this.ColCount = inpt[1];

        Dictionary<char, int> cnt = new Dictionary<char, int>();
        for (int i = 0; i < RowCount; i++) {
            string tmp = Reader.ReadLine();
            for (int j = 0; j < tmp.Length; j++) {
                if(cnt.ContainsKey(tmp[j])) {
                    cnt[tmp[j]]++;
                } else {
                    cnt[tmp[j]] = 1;
                }
            }
        }

        bool ans = Judge(cnt, new char[this.RowCount, this.ColCount]);
        string ansText = ans ? "Yes" : "No";
        Console.WriteLine(ansText);

    }

    private int RowCount;
    private int ColCount;
    private bool Judge(Dictionary<char, int> charList, char[,] map) {

        if(charList.Max(a=>a.Value) == 0) {
            return true;
        }

        int currentRow = -1;
        int currentCol = -1;
        for (int i = 0; i < RowCount; i++) {
            for (int j = 0; j < ColCount; j++) {
                if(map[i,j] == 0) {
                    currentRow = i;
                    currentCol = j;
                    break;
                }
            }
            if(currentRow >= 0) {
                break;
            }

        }

        int subRow = RowCount - currentRow - 1;
        int subCol = ColCount - currentCol - 1;
        char[] keys = charList.Where(a => a.Value > 0).Select(a => a.Key).ToArray();
        foreach(char next in keys) {
            if(subRow != currentRow && subCol != currentCol) {
                if(charList[next] < 4) {
                    continue;
                }
                map[currentRow, currentCol] = next;
                map[currentRow, subCol] = next;
                map[subRow, currentCol] = next;
                map[subRow, subCol] = next;
                charList[next] -= 4;
                if(Judge(charList, map)) {
                    return true;
                }
				map[currentRow, currentCol] = (char)0;
				map[currentRow, subCol] = (char)0;
				map[subRow, currentCol] = (char)0;
				map[subRow, subCol] = (char)0;
				charList[next] += 4;
			} else if(subRow != currentRow) {
                if(charList[next] < 2) {
                    continue;
                }
				map[currentRow, currentCol] = next;
				map[subRow, currentCol] = next;
				charList[next] -= 2;
				if (Judge(charList, map))
				{
					return true;
				}
				map[currentRow, currentCol] = (char)0;
				map[subRow, currentCol] = (char)0;
				charList[next] += 4;
			} else if(subCol != currentCol) {
                if(charList[next] <2 ) {
                    continue;
                }
				map[currentRow, currentCol] = next;
				map[currentRow, subCol] = next;
				charList[next] -= 2;
				if (Judge(charList, map))
				{
					return true;
				}
				map[currentRow, currentCol] = (char)0;
				map[currentRow, subCol] = (char)0;
				charList[next] += 2;
			} else {
				map[currentRow, currentCol] = next;
				charList[next] -= 1;
				if (Judge(charList, map))
				{
					return true;
				}
				map[currentRow, currentCol] = (char)0;
				charList[next] += 1;
			}
        }

        return false;

    }


    public class Reader
	{
		private static StringReader sr;
		public static bool IsDebug = false;
		public static string ReadLine()
		{
			if (IsDebug)
			{
				if (sr == null)
				{
					sr = new StringReader(InputText.Trim());
				}
				return sr.ReadLine();
			}
			else
			{
				return Console.ReadLine();
			}
		}
		private static string InputText = @"


2 5
abxba
abyba


";
	}

	public static void Main(string[] args)
	{
#if DEBUG
		Reader.IsDebug = true;
#endif
		Program prg = new Program();
		prg.Proc();
	}
}