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 void Main(string[] args)
		{
			var hw = Console.ReadLine().Split(' ').Select(int.Parse).ToArray();
			var dic = new Dictionary<char, int>();
			for (int i = 0; i < hw[0]; i++)
			{
				var input = Console.ReadLine();
				for(int j = 0;j < input.Length;j++)
				{
					if (dic.ContainsKey(input[j])) dic[input[j]]++;
					else dic.Add(input[j], 1);
				}
			}
			List<int> nokori = new List<int>();
			foreach(var a in dic)
			{
				if (a.Value % 4 != 0) nokori.Add(a.Value % 4);
			}
			bool ans = true;
			if(hw[1] % 2 == 0 && hw[0] % 2 == 0)
			{
				ans = nokori.Count == 0;
			}
			else if(hw[1] % 2 != 0 && hw[0] % 2 != 0)
			{
				int c = 0;
				foreach(var a in nokori)
				{
					if (a % 2 != 0) c++;
				}
				
				ans = (nokori.Sum() <= hw[0] + hw[1] - 1) && (c <= 1);
			}
			else
			{
				ans = nokori.All(x => x % 2 == 0);
				if (hw[0] % 2 == 0 && hw[0] < nokori.Sum()) ans = false;
				if (hw[1] % 2 == 0 && hw[1] < nokori.Sum()) ans = false;
			}
			if (ans) Console.WriteLine("Yes");
			else Console.WriteLine("No");
			//Console.ReadLine();
		}
	}
}