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: Runtime Error)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		int[] cnt = new int[26];
		for(int i=0;i<N;i++){
			for(int j=0;j<N;j++) cnt[S[i][j] - 'a']++;
		}
		
		if(N % 2 == 0 && M % 2 == 0){
			bool chk = true;
			for(int i=0;i<26;i++) if(cnt[i] % 4 != 0) chk = false;
			Console.WriteLine(chk ? "Yes" : "No");
			return;
		}
		if(N % 2 == 1 && M % 2 == 1){
			int n4 = (N / 2) * (M / 2);
			int n2 = (N / 2) + (M / 2);
			for(int i=0;i<26;i++){
				if(n4 == 0) break;
				int nn = cnt[i] / 4;
				n4 -= Math.Min(n4,nn);
				cnt[i] -= 4 * nn;
			}
			if(n4 != 0){
				Console.WriteLine("No");
				return;
			}
			for(int i=0;i<26;i++){
				if(n2 == 0) break;
				int nn = cnt[i] / 2;
				n2 -= Math.Min(n2,nn);
				cnt[i] -= 2 * nn;
			}
			if(n2 != 0){
				Console.WriteLine("No");
				return;
			}
			Console.WriteLine("Yes");
			return;
		}
		
		if(N % 2 == 0 && M % 2 == 1){
			int n4 = (N / 2) * (M / 2);
			int n2 = (N / 2) ;
			for(int i=0;i<26;i++){
				if(n4 == 0) break;
				int nn = cnt[i] / 4;
				n4 -= Math.Min(n4,nn);
				cnt[i] -= 4 * nn;
			}
			if(n4 != 0){
				Console.WriteLine("No");
				return;
			}
			for(int i=0;i<26;i++){
				if(n2 == 0) break;
				int nn = cnt[i] / 2;
				n2 -= Math.Min(n2,nn);
				cnt[i] -= 2 * nn;
			}
			if(n2 != 0){
				Console.WriteLine("No");
				return;
			}
			Console.WriteLine("Yes");
			return;
		}
		
		
		if(N % 2 == 1 && M % 2 == 0){
			int n4 = (N / 2) * (M / 2);
			int n2 = (M / 2) ;
			for(int i=0;i<26;i++){
				if(n4 == 0) break;
				int nn = cnt[i] / 4;
				n4 -= Math.Min(n4,nn);
				cnt[i] -= 4 * nn;
			}
			if(n4 != 0){
				Console.WriteLine("No");
				return;
			}
			for(int i=0;i<26;i++){
				if(n2 == 0) break;
				int nn = cnt[i] / 2;
				n2 -= Math.Min(n2,nn);
				cnt[i] -= 2 * nn;
			}
			if(n2 != 0){
				Console.WriteLine("No");
				return;
			}
			Console.WriteLine("Yes");
			return;
		}
		
		
		
		
		
		
	}
	int N,M;
	String[] S;
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1];
		S = new String[N];
		for(int i=0;i<N;i++) S[i] = rs();
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}