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.Linq;
using System.Diagnostics;
using System.Collections.Generic;
using static System.Math;

class P
{
    static void Main()
    {
        int[] hw = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int[] count = new int[26];
        for (int i = 0; i < hw[0]; i++)
        {
            foreach (char c in Console.ReadLine()) count[c - 'a']++;
        }
        int one = count.Count(x => x % 4 != 0 && x % 2 != 0);
        int two = count.Count(x => x % 4 != 0 && x % 2 == 0);
        bool flag;
        if (hw[0] % 2 == 1 && hw[1] % 2 == 1)
        {
            flag = one == 1 && hw[0] + hw[1] >= two && (hw[0] + hw[1] - two) % 2 == 0;
        }
        else if (hw[0] % 2 == 0 && hw[1] % 2 == 1)
        {
            flag = one == 0 && hw[0] >= two && (hw[0] - two) % 2 == 0;
        }
        else if (hw[0] % 2 == 1 && hw[1] % 2 == 0)
        {
            flag = one == 0 && hw[1] >= two && (hw[1] - two) % 2 == 0;
        }
        else
        {
            flag = one == 0 && two == 0;
        }
        Console.WriteLine(flag?"Yes":"No");
    }
}