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.Collections.Generic;
using System.Linq;
using System.Text;
class Program
{
    static void Main(string[] args)
    {
        int[] n = Console.ReadLine().Split().Select(int.Parse).ToArray();
        int[] a = new int[26];
        for (int i = 0; i < n[0]; i++)
        {
            string s = Console.ReadLine();
            for (int j = 0; j < s.Length; j++)
            {
                a[s[j] - 'a']++;
            }
        }
        if (n[0] == 1||n[1]==1) {
            bool already = false; for (int i = 0; i < 26; i++) {
                if (a[i] % 2 == 1) { if (already == false) { already = true; } else { Console.WriteLine("No"); } }
            }if (already) { Console.WriteLine("Yes"); return; }
            Console.WriteLine("No");return;
        }
        if (n[0] % 2 == 0 && n[1] % 2 == 0)
        {
            for (int i = 0; i < 26; i++)
            {
                if (a[i] % 4 != 0) { Console.WriteLine("No"); return; }
                
            }Console.WriteLine("Yes");return;
        }
        if (n[0] % 2 == 1 && n[1] % 2 == 1)
        {int twos = 0;
            int ones = 0;
            int fours = 0;
            for (int i = 0; i < 26; i++)
            {
                if (a[i] % 4 == 1) { ones++; }
                if (a[i] % 4 == 2) { twos++; }
                if (a[1] % 4 == 4) { fours++; }
            }
            if (ones + twos + fours == n[0] * n[1] && ones == 1 && twos == 2) { Console.WriteLine("Yes"); }
            else { Console.WriteLine("No"); }

        }
    }
//    static bool 
}