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: Accepted)


import java.util.Scanner;

public class Main {
	
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		
		int h = Integer.parseInt(sc.next());
		int w = Integer.parseInt(sc.next());
		
		int []alp = new int [26];
		
		for(int i = 0 ; i < h ;i++) {
			String s = sc.next();
			for(int j = 0 ; j < w ;j++) {
				int m = s.charAt(j) - 'a';
				alp[m]++;
			}
		}
		
		int m1 = 0;
		int m2 = 0;
		int m4 = h*w;
		
		if(h % 2 == 1 && w % 2 == 1) {
			m1 = 1;
			m2 = h + w - 2;
			m4 -= m2 + m1;
		}
		else if(h % 2 ==1) {
			m1 = 0;
			m2 = w;
			m4 -= m2 + m1;
		}
		else if(w % 2 == 1) {
			m1 = 0;
			m2 = h;
			m4 -= m1 + m2;
		}
		
		for(int i = 0 ; i < m1 ;i++) {
			for(int j = 0 ; j < 26 ;j++) {
				if(alp[j] % 2 == 1) {
					alp[j]--;
					break;
				}
			}
		}
		while(m2 > 0) {
			boolean jdg = false;
			for(int i = 0 ; i < 26 ;i++) {
				if(alp[i] % 4 == 2) {
					jdg = true;
					alp[i] -= 2;
					m2 -= 2;
					break;
				}
			}
			if(!jdg) break;
		}
		
		while(m4 > 0) {
			boolean jdg = false;
			for(int i = 0 ; i < 26 ;i++) {
				if(alp[i] % 4 == 0 && alp[i] != 0) {
					jdg = true;
					alp[i] -= 4;
					m4 -= 4;
					break;
				}
			}
			if(!jdg)break;
		}
		
		int cnt = 0;
		
		for(int i = 0 ; i < 26 ;i++) {
			if(alp[i] % 4 != 0) {
				System.out.println("No");
				return;
			}
			if(alp[i] % 4 == 0 && alp[i] != 0) {
				cnt += alp[i];
			}
		}
		System.out.println((cnt == m2)? "Yes" : "No");
	}
}