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: Accepted)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Text;
using System.Linq;
using static MyIO;


public class C
{
	public static void Main()
	{
		int H = GetInt();
		int W = GetInt();
		int[] num = new int[26];
		for(int i = 0; i < H; i++)
		{
			string a = GetString();
			for(int j = 0; j < W; j++)
				num[(int)(a[j] - 'a')]++;
		}

		int g1 = ((H % 2 == 1) && (W % 2 == 1)) ? 1 : 0;
		int g2 = ((H % 2 == 1) ? W / 2 : 0) + ((W % 2 == 1) ? H / 2 : 0);
		int g4 = (H * W - g1 - 2 * g2) / 4;

		if(g1 == 1)
		{
			int c = Array.FindIndex(num, x => x % 2 == 1);
			if(c != -1)
				num[c]--;
		}

		while(g2 > 0)
		{
			int c = Array.FindIndex(num, x => x % 4 == 2);
			if(c == -1)
			{
				g4 += g2 / 2;
				break;
			}
			else
			{
				num[c] -= 2;
				g2--;
			}
		}

		while(g4 > 0)
		{
			int c = Array.FindIndex(num, x => x > 0);
			if(c == -1)
			{
				break;
			}
			else
			{
				num[c] -= 4;
				g4--;
			}
		}

		Console.WriteLine(num.Any(x => x > 0) ? "No" : "Yes");
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}