In the center of the universe the origin of the chaos resides: a blind and crazy god called Azathoth. In his madness, Azathoth writes the numbers in basis 50, and each of the digits in basis 50 is written in binary basis. Moreover, he writes a dot in the beginning, in the end and between each digit.

For instance, 115 = 2 · 50^{1} + 15 · 50^{0}. As 2 in binary basis is |10|,
and 15 in binary basis is |1111|, Azathoth would write “`.10.1111.`”.

Your task is to write a program that prints each given number with the Azathoth system.

**Observation**

Your program must implement and use the procedure

that prints any natural number |n| in binary (zero included).

**Hint**

Use recursion.

**Input**

The input is a sequence of natural numbers.

**Output**

Your program must print each natural number in decimal and also in Azathoth system one per line and following the format of the instances.

Public test cases

**Input**

115 6 31 49 50 51 2532 0 1 1122334455

**Output**

115 = .10.1111. 6 = .110. 31 = .11111. 49 = .110001. 50 = .1.0. 51 = .1.1. 2532 = .1.0.100000. 0 = .0. 1 = .1. 1122334455 = .11.11101.11100.100001.100111.101.

**Input**

6250000

**Output**

6250000 = .1.0.0.0.0.

Information

- Author
- Professorat de P1
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++