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 Lua (5.3.2) (judge verdict: Accepted)

local s = io.read()
local function j(z)
  local n = #z
  for i = 1, n do
    if z:sub(i, i) ~= z:sub(n + 1 - i, n + 1 - i) then
      return false
    end
  end
  return true
end

local s1 = s:sub(1, (#s - 1) // 2)
local s2 = s:sub((#s + 3) // 2, #s)
local f = j(s) and j(s1) and j(s2)
print(f and "Yes" or "No")