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.Linq;

namespace CodeFestival2017qualAC
{
    class Program
    {
        static void Main(string[] args)
        {
            int[] ints = Console.ReadLine().Split(' ').Select(a => int.Parse(a)).ToArray();
            int H = ints[0];
            int W = ints[1];

            string[] matrix = new string[H];
            for (int i = 0; i < H; i++)
            {
                matrix[i] = Console.ReadLine();
            }

            int wildCard = 0;
            int pairs = 0;
            if (H % 2 == 1 & W % 2 == 1)
            {
                wildCard = 1;
                pairs = W / 2 + H / 2;
            } else if (H % 2 == 1)
            {
                pairs = W / 2;
            } else if (W % 2 == 1)
            {
                pairs = H / 2;
            }

            int[] counts = new int[26];
            for (int i = 0; i < H; i++)
            {
                for (int j = 0; j < W; j++)
                {
                    counts[matrix[i][j] - 'a']++;
                }
            }

            for (int i = 0; i < 26; i++)
            {
                counts[i] %= 4;
                if (counts[i] == 0)
                {
                    continue;
                }

                if (counts[i] == 2)
                {
                    pairs--;
                }

                if (counts[i] % 2 == 1)
                {
                    wildCard--;
                }
            }

            if (pairs < 0 | wildCard < 0)
            {
                Console.WriteLine("No");
                return;
            }
            Console.WriteLine("Yes");
        }
    }
}