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 System.Text;

class Program
{
    private int H,W;
    private int[] Count=new int[200];
    public void Solve()
    {
        var l=Console.ReadLine().Split(' ');
        H=int.Parse(l[0]);
        W=int.Parse(l[1]);
        for(int i=0;i<H;i++)
        {
            foreach(char c in Console.ReadLine())
            {
                Count[c]++;
            }
        }
        
        int two=0,one=0;
        foreach(int i in Count)
        {
            if(i%2==1)
            {
                one++;
            }
            if(i%4==2||i%4==3)
            {
                two++;
            }
        }
        if(H%2==1&&W%2==1)
        {
            if(one!=1)
            {
                Console.WriteLine("No");
                return;
            }
        }
        else
        {
            if(one!=0)
            {
                Console.WriteLine("No");
                return;
            }
        }
        int tt=0;
        if(H%2==1)
        {
            tt+=W/2;
        }
        if(W%2==1)
        {
            tt+=H/2;
        }
        if(tt<two||(tt-two)%2==1)
        {
            Console.WriteLine("No");
        }
        Console.WriteLine("Yes");
    } 
    
    static void Main()
    {
        new Program().Solve();
    }
}