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2017-09-13 17:00 CEST

Aleague#012

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2017-09-13 20:30 CEST
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Problem C
Tajna

Every evening, little Ivica sends secret messages to little Marica through e-mail. Knowing Ivica’s e-letter travels unguarded through the network on its way to Marica’s e-mailbox, they have decided to encrypt every message using the following algorithm:

  • Suppose Ivica’s message consists of $N$ characters.

  • Ivica must first find a matrix consisting of $R$ rows and $C$ columns such that $R \le C$ and $R \cdot C = N$. If there is more than one such matrix, Ivica chooses the one with the most rows.

  • Ivica writes his message into the matrix in row-major order. In other words, he writes the first segment of the message into the first row, the second segment into the second row and so on.

  • The message he sends to Marica is the matrix read in column-major order.

For instance, suppose Ivica wants to send the message “bombonisuuladici” containing 16 letters. He can use a $1 \times 16$, $2 \times 8$, or $4 \times 4$ matrix. Of these, the $4 \times 4$ has the most rows. When the message is written into it, the matrix looks like this, and the encrypted message becomes “boudonuimilcbsai”.

b

o

m

b

o

n

i

s

u

u

l

a

d

i

c

i

Marica has grown tired of spending her precious time deciphering Ivica’s messages, so you must write a program to do it for her.

Input

The input contains the received message, a string of lowercase letters of the English alphabet (with no spaces). The number of letters will be between 1 and 100.

Output

Output the original (decrypted) message.

Sample Input 1 Sample Output 1
bok
bok
Sample Input 2 Sample Output 2
koaski
kakosi
Sample Input 3 Sample Output 3
boudonuimilcbsai
bombonisuuladici