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 Ruby (2.3.3) (judge verdict: Wrong Answer)

S = gets
N = S.length

f1 = true
n1 = (N - 1) / 2

for i in 0..n1 - 1
  if S[i] != S[n1 - 1 - i]
    f1 = false
  end
end

f2 = true
n2 = (S.length + 3) / 2

for i in n2 - 1..N - 1
  if S[i] != S[n2 - 1 + (N - 1 - i)]
    f2 = false
  end
end

if f1 && f2
  puts "Yes"
elsif puts "No"
end