Rail Fence Cipher Decryption

The rail fence cipher is a basic transposition cipher. In this cipher, the plaintext is written in a zigzag pattern on a number of rows (rails) and then read row by row to produce the ciphertext. For example, if we take the plaintext Hello,World! and write it in a rail fence of height h = 3, we arrange the characters as follows:

H   o   r
 e l , o l !
  l   W   d

The ciphertext is obtained by reading each row from left to right: first row gives Hor, second gives el,ol! and third gives lWd. Hence, the final ciphertext is Horel,ol!lWd.

In general, if the ciphertext formed by writing in a rail fence of height h is given, we can retrieve the original plaintext by reconstructing the zigzag pattern. The indices follow a pattern that can be formally described by the formula: \[ pattern(i)=\begin{cases} i\quad,&\text{if } h=1,\\ \text{zigzag } 0\to h-1 \text{ and back},&\text{if } h>1. \end{cases} \]

Your task is: Given the height h and a ciphertext string s (encrypted as described above), output the original plaintext string.

inputFormat

The input consists of two lines:

• The first line contains an integer h representing the height of the rail fence.
• The second line contains a non-empty string s which is the ciphertext.

outputFormat

Output a single line: the decrypted plaintext string.

sample

3
Horel,ol!lWd

Hello,World!