题目描述
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
输入格式
见题面
输出格式
见题面
样例输入
2 5
abxba
abyba
样例输出
No