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 cf
{
    class Program
    {
        static void Main(string[] args)
        {
            int H, W;
            string[] s = Console.ReadLine().Split(' ');
            H = int.Parse(s[0]);
            W = int.Parse(s[1]);

            string str;
            int[] alp = new int[26];
            for (int i = 0; i < H; i++)
            {
                str = Console.ReadLine();
                for (int j = 0; j < W; j++)
                {
                    alp[str[j] - 'a'] += 1;
                }
            }

            int h = H / 2;
            int w = W / 2;

            int quate = h * w;
            int p, qt = 0;
            int odd = 0;
            for (int i = 0; i < 26; i++)
            {
                if (alp[i] == 0) continue;
                p = alp[i] / 4;
                qt += p;
                alp[i] -= p * 4;
                if (quate < qt)
                {
                    alp[i] += (qt + p - quate) * 4;
                }
                if (alp[i] % 2 == 1)
                {
                    odd += 1;
                }
            }

            if(quate > qt)
            {
                Console.WriteLine("No");
            }
            else if (odd > 1)
            {
                Console.WriteLine("No");
            }
            else if (H % 2 == 0 && W % 2 == 0 && odd == 1)
            {
                Console.WriteLine("No");
            }
            else
            {
                Console.WriteLine("Yes");
            }
        }
    }
}