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.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace CF2016
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');
            int H = int.Parse(str[0]);
            int W = int.Parse(str[1]);
            int[] n = new int[26];
            for(int i = 0; i < H; i++)
            {
                string s = Console.ReadLine();
                for(int j = 0; j < W; j++)
                {
                    n[s[j] - 'a']++;
                }
            }
            int x = 0;
            int f = 0;
            if (H % 2 == 0 && W % 2 == 0)
            {
                for(int i = 0; i < 26; i++)
                {
                    if (n[i] % 4 != 0)
                    {
                        f++;
                        break;
                    }
                }
            }else if (H == 1||W==1)
            {
                for (int i = 0; i < 26; i++)
                {
                    if (n[i] % 2 != 0)
                    {
                        x++;
                    }
                }
                if (x > 1)
                {
                    f++;
                }
            }else if (H % 2 == 1 && W % 2 == 1)
            {
                int o = 0;
                for (int i = 0; i < 26; i++)
                {
                    if (n[i] % 2 == 1)
                    {
                        o++;
                    }
                    else if (n[i] % 4 != 0)
                    {
                        x++;
                    }
                }
                if (!(o == 1 && x <= (H / 2 + W / 2)))
                {
                    f++;
                }
            }
            else if (H % 2 == 1) 
            {
                for (int i = 0; i < 26; i++)
                {
                    if (n[i] % 2 == 1)
                    {
                        f++;
                    }
                    else if (n[i] % 4 != 0)
                    {
                        x++;
                    }
                }
                if (x > W / 2)
                {
                    f++;
                }
            }
            else
            {
                for (int i = 0; i < 26; i++)
                {
                    if (n[i] % 2 == 1)
                    {
                        f++;
                    }
                    else if (n[i] % 4 != 0)
                    {
                        x++;
                    }
                }
                if (x > H / 2)
                {
                    f++;
                }
            }

            //
            if (f == 0)
            {
                Console.WriteLine("Yes");
            }
            else
            {
                Console.WriteLine("No");
            }

        }
    }
}