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;

class CF2017QAC
{
	static public void Main(string[] args)
	{
		int H, W;
		string[] vals = Console.ReadLine().Split(' ');
		H = int.Parse(vals[0]);
		W = int.Parse(vals[1]);
		int[] count = new int[26];
		string line;
		for(int i=0; i<H; i++)
		{
			line = Console.ReadLine();
			for(int j=0; j<W; j++)
			{
				count[line[j]-'a']++;
			}
		}
		
		int c4, c2, c1;
		if(H % 2 == 0 && W % 2 == 0)
		{
			c4 = H * W;
			c2 = c1 = 0;
		}
		else if(H % 2 == 1 && W % 2 == 0)
		{
			c2 = W;
			c4 = H * W - W;
			c1 = 0;
		}
		else if(H % 2 == 0 && W % 2 == 1)
		{
			c2 = H;
			c4 = H * W - H;
			c1 = 0;
		}
		else
		{
			c2 = H + W - 2;
			c4 = H * W - (H + W - 1);
			c1 = 1;
		}

		for(int i=0; i<26; i++)
		{
			while(count[i] >= 4 && c4 >= 4)
			{
				count[i] -= 4;
				c4 -= 4;
			}
		}
		if(c4 != 0)
		{
			Console.WriteLine("No");
			return;
		}

		for(int i=0; i<26; i++)
		{
			while(count[i] >= 2 && c2 >= 2)
			{
				count[i] -= 2;
				c2 -= 2;
			}
		}
		if(c2 != 0)
		{
			Console.WriteLine("No");
			return;
		}

		if(c1 == 1)
		{
			for(int i=0; i<26; i++)
			{
				if(count[i] == 1)
				{
					count[i]--;
					c1--;
					break;
				}
			}
		}
		if(c1 != 0)
		{
			Console.WriteLine("No");
			return;
		}


		Console.WriteLine("Yes");
	}
}