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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Text;
using System.Collections.Generic;
using System.Collections;
using System.Linq;
using E = System.Linq.Enumerable;
using System.Runtime.InteropServices.ComTypes;

class Program
{
    static char[] abc = "abcdefghijklmnopqrstuvwxyz".ToCharArray();
    static long mod = 1000000007;
    static void Main(string[] args)
    {
        var HW = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToArray();
        var H = HW[0];
        var W = HW[1];

        var map = new String[H];
        for (int i = 0; i < H; i++)
        {
            map[i] = Console.ReadLine();
        }

        var dic = new Dictionary<char, long>();
        for (int i = 0; i < H; i++)
        {
            for (int j = 0; j < W; j++)
            {
                if (dic.ContainsKey(map[i][j]))
                {
                    dic[map[i][j]]++;
                }
                else
                {
                    dic.Add(map[i][j], 1);
                }
            }
        }

        long one = (H * W) % 2 == 0 ? 0 : 1;

        long two = (H % 2 == 0 ? 0 : W) + (W % 2 == 0 ? 0 : H) - 2 * one;
        long four = (H * W - one - two) / 4;
        two /= 2;

        var Sorted = dic.OrderBy((x) => x.Value);
        var ans = true;

        var a = 0L;
        var b = 0L;
        var c = 0L;

        foreach (var item in Sorted)
        {
            var res = item.Value;
            a += res / 4;
            b += (res % 4) / 2;
            c += ((res % 4) % 2);
        }

        if (four <= a)
        {
            a -= four;
            b += a / 2;
        }
        else
        {
            ans = false;
        }

        if (two <= b)
        {
            b -= two;
            c += b / 2;
        }
        else
        {
            ans = false;
        }

        if (c != one)
        {
            ans = false;
        }
        Console.WriteLine(ans ? "Yes" : "No");
    }



}