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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;
import java.io.*;

public class Main{

	public static void main(String[] args){
		solve();
	}

	public static void solve(){
		Scanner sc = new Scanner(System.in);
		int h = sc.nextInt();
		int w = sc.nextInt();
		int[] counter = new int[26];
		String[] a = new String[h];
		for(int i=0;i<h;i++){
			a[i] = sc.next();
			for(int j=0;j<w;j++){
				counter[(int)a[i].charAt(j)-(int)'a']++;
			}
		}
		int one = 0;
		int two = 0;
		if(h%2==1 && w%2==1){
			one = 1;
			two = h + w - 2;
		}
		else if(h%2==1){
			two = w;
		}
		else if(w%2==1){
			two = h;
		}
		
		int four = h*w-two-one;
		//System.out.println(four+" "+two+" "+one);
		for(int i=0;i<26;i++){
			if(counter[i]>=4){
				counter[i] -= 4;
				i--;
				four-=4;
			}
			if(four==0){
				break;
			}
		}
		for(int i=0;i<26;i++){
			if(counter[i]>=2){
				counter[i] -= 2;
				i--;
				two-=2;
			}
			if(two==0){
				break;
			}
		}
		for(int i=0;i<26;i++){
			if(counter[i]>=1){
				counter[i] -= 1;
				i--;
				one--;
			}
			if(one==0){
				break;
			}
		}
		boolean flag = true;
		for(int i=0;i<26;i++){
			if(counter[i]!=0){
				flag = false;
			}
		}
		if(flag){
			System.out.println("Yes");
		}
		else{
			System.out.println("No");
		}
	}
}