# P0018. Azathoth numbers P53202

Statement html

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 · 501 + 15 · 500. 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

void binary_print(int n);

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++