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: Accepted)

using System;
using System.Collections.Generic;
using System.Text;

namespace AtTest._400Problems_remain_
{
    class CF2017Final_C
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            int[] hw = ReadInts();
            int h = hw[0];
            int w = hw[1];
            int[] counts = new int[26];
            for (int i = 0; i < h; i++)
            {
                string s = Read();
                for (int j = 0; j < w; j++)
                {
                    counts[s[j] - 'a']++;
                }
            }
            Array.Sort(counts);
            Array.Reverse(counts);
            int count1 = (h % 2) * (w % 2);
            int count2 = (w / 2) * (h % 2) + (h / 2) * (w % 2);
            int count4 = (h / 2) * (w / 2);
            for (int i = 0; i < counts.Length; i++)
            {
                int minusCount;
                minusCount = Math.Min(counts[i] / 4, count4);
                count4 -= minusCount;
                counts[i] -= minusCount * 4;
                minusCount = Math.Min(counts[i] / 2, count2);
                count2 -= minusCount;
                counts[i] -= minusCount * 2;
                minusCount = Math.Min(counts[i], count1);
                count1 -= minusCount;
                counts[i] -= minusCount;
                if (counts[i] > 0)
                {
                    Console.WriteLine("No");
                    return;
                }
            }
            Console.WriteLine("Yes");
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}