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: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Convert;
using static System.Math;
//using static System.Globalization.CultureInfo;

class Program
{
    static void Main(string[] args)
    {
        var hw = Input.ar;
        var gred = Enumerable.Repeat(0, hw[0]).Select(v => ReadLine()).ToArray();
        var g = new[] { 0, 0, hw[0]/2 * (hw[1] /2)  };
        if (hw[0] % 2 == 1 && hw[1] % 2 == 1)
            g[0] = 1;
        if (hw[0] % 2 != 0 || hw[1] % 2 != 0)
            g[1] = (hw[0]-1) / 2 + (hw[1]-1)/2;
        var dic = new Dictionary<char, int>();
        for (var i = 0; i < hw[0]; i++)
            for (var j = 0; j < hw[1]; j++)
                if (dic.ContainsKey(gred[i][j]))
                    dic[gred[i][j]]++;
                else dic[gred[i][j]] = 1;
        for(var i=0;i<3;i++)
            for(var j = 0; j < g[i]; j++)
            {
                foreach (var pair in dic)
                {
                    if (pair.Value == 0) continue;
                    if (i == 0 && pair.Value % 4 % 2 == 1)
                    {
                        dic[pair.Key] -= 1;
                        break;
                    }
                    if (i == 1 && pair.Value % 4 == 2)
                    {
                        dic[pair.Key] -= 2;
                        break;
                    }
                    if (i == 2 && pair.Value % 4 == 0)
                    {
                        dic[pair.Key] -= 4;
                        break;
                    }
                }
            }
        foreach (var pair in dic)
            if (pair.Value != 0)
            {
                WriteLine("No");
                return;
            }
        WriteLine("Yes");
    }
}

public class Input
{
    public static string read => ReadLine();
    public  static int[] ar => Array.ConvertAll(read.Split(' '), int.Parse);
    public  static int num => ToInt32(read);
    public static long[] arL => Array.ConvertAll(read.Split(' '), long.Parse);
    public  static long numL => ToInt64(read);
    public static int[][] twodim(int num)
        => Enumerable.Repeat(0, num).Select(v => ar).ToArray();
    public static long[][] twodimL(int num)
        => Enumerable.Repeat(0, num).Select(v => arL).ToArray();
    public  const string Alfa = "abcdefghijklmnopqrstuvwxyz";
    public  const int MOD = 1000000007;
}