String Palindrome

A string S of an odd length is said to be a strong palindrome if and only if all of the following conditions are satisfied:

• S is a palindrome.
• Let N be the length of S. The string formed by the 1-st through ((N-1)/2)-th characters of S is a palindrome.
• The string consisting of the (N+3)/2-st through N-th characters of S is a palindrome.

Determine whether S is a strong palindrome.

Constraints

• S consists of lowercase English letters.
• The length of S is an odd number between 3 and 99 (inclusive).

Input

Input is given from Standard Input in the following format:

S

Output

If S is a strong palindrome, print Yes; otherwise, print No.

Examples

Input

akasaka

Output

Yes

Input

level

Output

No

Input

atcoder

Output

No

inputFormat

Input

Input is given from Standard Input in the following format:

S

outputFormat

Output

If S is a strong palindrome, print Yes; otherwise, print No.

Examples

Input

akasaka

Output

Yes

Input

level

Output

No

Input

atcoder

Output

No

样例

akasaka

Yes