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

public class Hello
{
    public static void Main()
    {
        var d = new Dictionary<char, int>();
        string[] line = Console.ReadLine().Trim().Split(' ');
        var h = int.Parse(line[0]);
        var w = int.Parse(line[1]);
        for (int i = 0; i < h; i++)
        {
            var s = Console.ReadLine().Trim();
            for (int j = 0; j < w; j++)
                if (d.ContainsKey(s[j])) d[s[j]]++;
                else d[s[j]] = 1;
        }
        var a = new int[d.Count()];
        var p = 0;
        foreach (var x in d) a[p++] = x.Value;
        var kg = 0;
        if (h % 2 == 0) kg++;
        if (w % 2 == 0) kg++;
        bool ret;
        if (kg == 2) ret = checkGG(a);
        else if (kg == 1) ret = checkKG(h, w, a);
        else ret = checkKK(h, w, a);
        Console.WriteLine(ret ? "Yes" : "No");
    }
    public static bool checkKK(int h, int w, int[] a)
    {
        if (h == 1 && w == 1) return true;
        var c4 = 0;
        var c2 = 0;
        for (int i = 0; i < a.Length; i++)
        {
            c4 += a[i] / 4;
            a[i] %= 4;
            c2 += a[i] / 2;
            a[i] %= 2;
        }
        if (h == 1 | w == 1)
        {
            c2 += 2 * c4;
            return c2 == h / 2 + w / 2;
        }
        else
        {
            var ww = (h * w - (h + w - 1)) / 4;
            if (c4 >= ww) c2 += (c4 - ww) * 2;
            else return false;
            var ww2 = (h + w - 1) / 2;
            return c2 == ww2;
        }
    }
    public static bool checkKG(int h, int w, int[] a)
    {
        var c4 = 0;
        for (int i = 0; i < a.Length; i++)
        {
            if (a[i] % 2 == 1) return false;
            c4 += a[i] / 4;
            a[i] %= 4;
        }
        var zc4 = h / 2 + w / 2 - 1;
        return c4 >= zc4;
    }
    public static bool checkGG(int[] a)
    {
        for (int i = 0; i < a.Length; i++)
            if (a[i] % 4 != 0) return false;
        return true;
    }
}