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: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using System.Globalization;
using System.Diagnostics;



class Myon
{
    public Myon() { }
    public static int Main()
    {
        new Myon().calc();
        return 0;
    }
    

    Scanner cin;
    
    void calc()
    {
        if (check()) Console.WriteLine("YES");
        else Console.WriteLine("NO");
    }

    bool check()
    {
        cin = new Scanner();
        Dictionary<char, int> dic = new Dictionary<char, int>();
        int H = cin.nextInt();
        int W = cin.nextInt();
        for (int i = 0; i < H; i++)
        {
            string S = cin.next();
            for (int j = 0; j < W; j++)
            {
                if (!dic.ContainsKey(S[j])) dic[S[j]] = 0;
                dic[S[j]]++;
            }
        }
        int Num4 = 0;
        int Num2 = 0;
        int Num1 = 0;
        foreach (var item in dic.Values)
        {
            Num4 += item / 4;
            Num2 += (item % 4) / 2;
            Num1 += (item % 2) / 1;
        }

        int Need4 = 0;
        int Need2 = 0;
        int Need1 = 0;
        for (int i = 0; i <= (H - 1) / 2; i++)
        {
            for (int j = 0; j <= (W - 1) / 2; j++)
            {
                Dictionary<int, int> tdic = new Dictionary<int, int>();
                tdic[i * 10000 + j] = 1;
                tdic[i * 10000 + (W - 1 - j)] = 1;
                tdic[(H -1 -i) * 10000 + j] = 1;
                tdic[(H - 1- i) * 10000 + (W - 1 - j)] = 1;
                if (tdic.Count == 4) Need4++;
                else if (tdic.Count == 2) Need2++;
                else Need1++;
            }
        }

        if (Need4 > Num4) return false;
        Need4 -= Num4;
        Num2 += Num4 * 2;
        if (Need2 > Num2) return false;
        return true;
    }
    
}



class Scanner
{
    string[] s;
    int i;

    char[] cs = new char[] { ' ' };

    public Scanner()
    {
        s = new string[0];
        i = 0;
    }

    public string next()
    {
        if (i < s.Length) return s[i++];
        string st = Console.ReadLine();
        while (st == "") st = Console.ReadLine();
        s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
        if (s.Length == 0) return next();
        i = 0;
        return s[i++];
    }

    public int nextInt()
    {
        return int.Parse(next());
    }
    public int[] ArrayInt(int N, int add = 0)
    {
        int[] Array = new int[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextInt() + add;
        }
        return Array;
    }

    public long nextLong()
    {
        return long.Parse(next());
    }

    public long[] ArrayLong(int N, long add = 0)
    {
        long[] Array = new long[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextLong() + add;
        }
        return Array;
    }

    public double nextDouble()
    {
        return double.Parse(next());
    }


    public double[] ArrayDouble(int N, double add = 0)
    {
        double[] Array = new double[N];
        for (int i = 0; i < N; i++)
        {
            Array[i] = nextDouble() + add;
        }
        return Array;
    }
}