Palindromic Matrix

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.

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.

Examples

Input

3 4 aabb aabb aacc

Output

Yes

Input

2 2 aa bb

Output

No

Input

5 1 t w e e t

Output

Yes

Input

2 5 abxba abyba

Output

No

Input

1 1 z

Output

Yes

inputFormat

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}

outputFormat

Output

If Snuke can create a matrix satisfying the condition, print Yes; otherwise, print No.

Examples

Input

3 4 aabb aabb aacc

Output

Yes

Input

2 2 aa bb

Output

No

Input

5 1 t w e e t

Output

Yes

Input

2 5 abxba abyba

Output

No

Input

1 1 z

Output

Yes

样例

2 5
abxba
abyba

No