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;

namespace CF2017qA
{
    class C
    {
        static void Main(string[] args)
        {
            //input
            int[] input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int H = input[0];
            int W = input[1];

            char[,] HW = new char[H, W];
            int[] cCount = new int[26];
            for (int h = 0; h < H; h++)
            {
                string a = Console.ReadLine();
                for (int w = 0; w < W; w++)
                {
                    HW[h, w] = a[w];
                    cCount[a[w] - 'a']++;
                }
            }

            if (H % 2 == 0 && W % 2 == 0)
            {
                for (int i = 0; i < cCount.Length; i++)
                {
                    if (cCount[i] % 4 != 0) { Console.WriteLine("No"); return; }
                }
                Console.WriteLine("Yes"); return;
            }

            if (H % 2 != 0 && W % 2 != 0)
            {
                for (int i = 0; i < cCount.Length; i++)
                {
                    cCount[i] %= 4;
                }

                int ecount = 0;
                int ocount = 0;
                for (int i = 0; i < cCount.Length; i++)
                {
                    if (cCount[i] != 0 && cCount[i] % 2 == 0) ecount++;
                    else if (cCount[i] % 2 != 0) ocount++;
                }

                if (ecount <= (W + H) / 2 && ocount == 1)
                {
                    Console.WriteLine("Yes"); return;
                }
                else
                {
                    Console.WriteLine("No"); return;
                }
            }

            if (H % 2 == 0 || W % 2 == 0)
            {
                for (int i = 0; i < cCount.Length; i++)
                {
                    cCount[i] %= 4;
                }

                int count = 0;
                for (int i = 0; i < cCount.Length; i++)
                {
                    if (cCount[i] != 0 && cCount[i] % 2 == 0) count++;
                    else if (cCount[i] % 2 != 0) { Console.WriteLine("No"); return; }
                }

                if (H % 2 == 0 && count <= H / 2)
                {
                    Console.WriteLine("Yes"); return;
                }
                else if (W % 2 == 0 && count <= W / 2)
                {
                    Console.WriteLine("Yes"); return;
                }
                else
                {
                    Console.WriteLine("No"); return;
                }

            }

            Console.WriteLine("Hello World!");
        }
    }
}