Kata

Introduction

A look-and-say sequence is an integer sequence. To generate a member of the sequence from the previous member, read off the digits of the previous member, counting the number of digits in groups of the same digit.

Examples:
1 ⇒ "one 1" ⇒ 11
21 ⇒ "one 2, one 1" ⇒ 1211

Starting with 1, the sequence begins with 1, 11, 21, 1211, 111221, 312211, 13112221, ...
Starting with 7, the sequence begins with 7, 17, 1117, 3117, 132117, 1113122117, ...

Task

Given a number $nn$, member of a look and say sequence, compute the starting number of the sequence, i.e. a number $ss$ such that:

• the input number $nn$ can be generated from $ss$ using 0 or more look and say steps
• $ss$ can't be generated from a different number using look and say algorithm

Note: In this kata all numbers (including starting numbers) contain at most 9 consecutive identical digits.

Input

• n [integer]

A member of a look and say sequence. Range: $00$–$10^{180}10^\{180\}$

Output [integer]

The starting number of the sequence.

Examples

• starting_number(2) ⇒ 2
2 can't be generated using look and say algorithm

• starting_number(23) ⇒ 333
23 is generated from 33
33 is generated from 333
333 can't be generated