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.Diagnostics;
using System.IO;
using System.Linq;
using System.Numerics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
public static class P
{
    public static void Main()
    {
        var hw = Console.ReadLine().Split().Select(int.Parse).ToArray();

        var map = Enumerable.Repeat(0, hw[0]).SelectMany(_ => Console.ReadLine()).ToArray();
        var chars = Enumerable.Range(0, 26).Select(x => map.Count(y => y - 'a' == x)).ToArray();
        bool cond;
        if (hw[0] % 2 == 0 && hw[1] % 2 == 0)
        {
            cond = chars.All(x => x % 4 == 0);
        }
        else if (hw[0] % 2 == 0 && hw[1] % 2 == 1 || hw[0] % 2 == 1 && hw[1] % 2 == 0)
        {
            var even = hw[1] % 2 == 1 ? hw[0] : hw[1];
            cond = chars.All(x => x % 2 == 0) && chars.Count(x => x % 4 != 0) <= even / 2;
        }
        else
        {
            var ind = chars.TakeWhile(x => x % 2 == 0).Count();
            if (ind == 26) cond = false;
            else
            {
                chars[ind]--;
                cond = chars.All(x => x % 2 == 0) && chars.Count(x => x % 4 != 0) <= (hw[0] / 2) + (hw[1] / 2);
            }
        }

        Console.WriteLine(cond ? "Yes" : "No");
    }
}