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 (7.4.4) (judge verdict: Accepted)

<?php
list($h, $w) = ints();
for ($i = 0; $i < $h; ++$i) {
    list($a) = strs();
    for ($j = 0; $j < $w; ++$j) {
        if (isset($cnt[$a[$j]])) ++$cnt[$a[$j]];
        else $cnt[$a[$j]] = 1;
    }
}

$g1 = $h % 2 && $w % 2 ? 1 : 0;
$g2 = ($w % 2) * intdiv($h, 2) + ($h % 2) * intdiv($w, 2);
$g4 = intdiv($h, 2) * intdiv($w, 2);

for ($i = 1; $i <= $g1; ++$i) {
    foreach ($cnt as $k => $v) {
        if ($v % 4 === 1 || $v % 4 === 3) {
            $cnt[$k] -= 1;
            continue 2;
        }
    }
    exit('No');
}

for ($i = 1; $i <= $g2; ++$i) {
    foreach ($cnt as $k => $v) {
        if ($v % 4 === 2) {
            $cnt[$k] -= 2;
            continue 2;
        }
    }
    foreach ($cnt as $k => $v) {
        if ($v > 0 && $v % 4 === 0) {
            $cnt[$k] -= 2;
            continue 2;
        }
    }
    exit('No');
}

for ($i = 1; $i <= $g4; ++$i) {
    foreach ($cnt as $k => $v) {
        if ($v > 0 && $v % 4 === 0) {
            $cnt[$k] -= 4;
            continue 2;
        }
    }
    exit('No');
}

echo 'Yes';
function strs()
{
    return explode(' ', trim(fgets(STDIN)));
}
function ints()
{
    return array_map('intval', explode(' ', trim(fgets(STDIN))));
}