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

public class Main {
    static InputStream is;
    static PrintWriter out;
    static String INPUT = "";
    
    static void solve()
    {
        int H = ni();
        int W = ni();

        char[][] map = nm(H,W);
        int[] a = new int[26];
        for(int i = 0; i < H; i++){
            for(int j = 0; j < W; j++){
                a[map[i][j]-'a']++;
            }
        }

        int g0 = 1;
        int g1 = (H/2)*(W/2);
        int g2 = (H % 2 == 1 ? W/2 : 0) + (W % 2 == 1 ? H/2 : 0);

        if(H % 2 == 0 || W % 2 == 0) g0--;

        for(int i = 0; i < 26; i++){
            if(a[i] % 2 == 1){
                a[i]--;
                g0--;
            }
        }
        for(int i = 0; i < 26; i++){
            if(a[i] >= 4){
                g1 -= a[i]/4;
                a[i] = a[i] - 4*(a[i]/4);
            }
        }
        for(int i = 0; i < 26; i++){
            if(a[i] >= 2){
                g2 -= a[i]/2;
                a[i] = a[i] - 2*(a[i]/2);
            }
            if(a[i] != 0){
                out.println("No");
                return;
            }
        }
        if(g2 != 0){
            out.println("No");
            return;
        }
        out.println("Yes");
    }
    
    public static void main(String[] args) throws Exception
    {
        long S = System.currentTimeMillis();
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
        
        solve();
        out.flush();
        long G = System.currentTimeMillis();
        tr(G-S+"ms");
    }
    
    private static boolean eof()
    {
        if(lenbuf == -1)return true;
        int lptr = ptrbuf;
        while(lptr < lenbuf)if(!isSpaceChar(inbuf[lptr++]))return false;
        
        try {
            is.mark(1000);
            while(true){
                int b = is.read();
                if(b == -1){
                    is.reset();
                    return true;
                }else if(!isSpaceChar(b)){
                    is.reset();
                    return false;
                }
            }
        } catch (IOException e) {
            return true;
        }
    }
    
    private static byte[] inbuf = new byte[1024];
    static int lenbuf = 0, ptrbuf = 0;
    
    private static int readByte()
    {
        if(lenbuf == -1)throw new InputMismatchException();
        if(ptrbuf >= lenbuf){
            ptrbuf = 0;
            try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
            if(lenbuf <= 0)return -1;
        }
        return inbuf[ptrbuf++];
    }
    
    private static boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
//  private static boolean isSpaceChar(int c) { return !(c >= 32 && c <= 126); }
    private static int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
    
    private static double nd() { return Double.parseDouble(ns()); }
    private static char nc() { return (char)skip(); }
    
    private static String ns()
    {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while(!(isSpaceChar(b))){
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }
    
    private static char[] ns(int n)
    {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while(p < n && !(isSpaceChar(b))){
            buf[p++] = (char)b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    
    private static char[][] nm(int n, int m)
    {
        char[][] map = new char[n][];
        for(int i = 0;i < n;i++)map[i] = ns(m);
        return map;
    }
    
    private static int[] na(int n)
    {
        int[] a = new int[n];
        for(int i = 0;i < n;i++)a[i] = ni();
        return a;
    }
    
    private static int ni()
    {
        int num = 0, b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static long nl()
    {
        long num = 0;
        int b;
        boolean minus = false;
        while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
        if(b == '-'){
            minus = true;
            b = readByte();
        }
        
        while(true){
            if(b >= '0' && b <= '9'){
                num = num * 10 + (b - '0');
            }else{
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    
    private static void tr(Object... o) { if(INPUT.length() != 0)System.out.println(Arrays.deepToString(o)); }

    private static int[] nsi(){
        char[] s = ns().toCharArray();
        int[] a = new int[s.length];
        for(int j = 0; j < s.length; j++){
           a[j] = s[j] - '0';
        }
        return a;
    }
}