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 AtCoder
{
    class Program
    {
        static bool Count(int[] values, int num, int step)
        {
            for (int i = 0; i < 26 && num > 0; ++i)
            {
                while (values[i] >= step && num > 0)
                {
                    values[i] -= step;
                    --num;
                }
            }
            return num == 0;
        }
        static bool Solve(int H, int W, string[] A)
        {
            var values = new int[26];
            foreach (string a in A)
            {
                foreach (char c in a)
                {
                    ++values[c - 'a'];
                }
            }
            if (!Count(values, (H / 2) * (W / 2), 4)) { return false; }
            if (!Count(values, (H / 2) * (W % 2), 2)) { return false; }
            if (!Count(values, (H % 2) * (W / 2), 2)) { return false; }
            if (!Count(values, (H % 2) * (W % 2), 1)) { return false; }
            return values.Sum() == 0;
        }
        static void Main(string[] args)
        {
            int[] V = Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
            int H = V[0];
            int W = V[1];
            var A = new string[H];
            for (int i = 0; i < H; ++i) { A[i] = Console.ReadLine(); }
            Console.WriteLine(Solve(H, W, A) ? "Yes" : "No");
        }
    }
}