Problem:
Score : 200 points

Problem Statement

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.

Sample Input 1

akasaka

Sample Output 1

Yes

S is akasaka.

The string formed by the 1-st through the 3-rd characters is aka.

The string formed by the 5-th through the 7-th characters is aka.
All of these are palindromes, so S is a strong palindrome.

Sample Input 2

level

Sample Output 2

No

Sample Input 3

atcoder

Sample Output 3

No

Solution in LuaJIT (2.0.4) (judge verdict: Wrong Answer)

local function no()
    print("no")
    os.exit()
end

local s = ""..io.read("*l")
if s ~= s:reverse() then
    no()
end
local front_s = s:sub(1, (s:len() - 1) / 2)
if front_s ~= front_s:reverse() then
    no()
end
local back_s = s:sub((s:len() + 3) / 2, s:len())
if back_s ~= back_s:reverse() then
    no()
end

print("yes")