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

• $1 \leq H, W \leq 100$
• $a_{ij}$ 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.

3 4
aabb
aabb
aacc

Yes

For example, the following matrix satisfies the condition.

abba
acca
abba

2 2
aa
bb

No

It is not possible to create a matrix satisfying the condition, no matter how we rearrange the elements in $A$.

5 1
t
w
e
e
t

Yes

For example, the following matrix satisfies the condition.

t
e
w
e
t

2 5
abxba
abyba

No

1 1
z

Yes