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 PHP (5.6.30) (judge verdict: Wrong Answer)

<?php
list($H, $W) = fscanf(STDIN, '%d %d\n');
$group1 = 1;
$group2 = floor($H/2) + floor($W/2);
$group3 = floor($H/2) * floor($W/2);
//O(H*M)
$chars = [];
for ($i=0;$i<$H;$i++){
    fscanf(STDIN,'%s',$str);
    foreach(str_split($str) as $value){
        if (array_key_exists($value, $chars)) {
            $chars[$value]++;
        } else {
            $chars[$value] = 1;
        }
    }
}

//O(N)
foreach ($chars as $char => $count){
    if ($count%4 === 1 || $count%4 === 3){
        $chars[$char]--;
        break;
    }
}

//O(N*group2)
for($i=0;$i<$group2;$i++){
    foreach ($chars as $char => $count){
        if ($count%4 === 2){
            $chars[$char] -=2;
            break;
        }
    }
}

//O(N*group3)
for($i=0;$i<$group3;$i++){
    foreach ($chars as $char => $count){
        if ($count%4 === 0){
            $chars[$char]-=4;
            break;

        }
    }
}

$sum = 0;
foreach($chars as $count){
    $sum += $count;
}

if ($sum === 0){
    echo 'Yes';
} else {
    echo 'No';
}