P0012. Diabolical numbers

We say that a number is diabolical if it is divisible for the double of the sum of its digits in basis 4. Your task is to write a program that, given a sequence of integers strictly positive finished in $-1$ , counts how many of them are diabolical.

Your program must include and use the function

    bool is_diabolical(int n);

that indicates if an integer |n| strictly positive is diabolical or is not.

These are some instances:

$n$	1	4	6	17	20	23	28	140	255	999999972
$n$ in basis 4	1	10	12	101	110	113	130	2030	3333	323212230213210
sum of the digits	1	1	3	2	2	5	4	5	12	27
diabolical	No	Yes	Yes	No	Yes	No	No	Yes	No	Yes

Input

The input consists of a sequence of integers strictly positive finished in $-1$ -

Output

Your program must print the quantity of diabolical numbers of the sequence, with six digits. (The inputs will always have less than a million diabolical numbers.)

Problem information

Author: Unknown
Translator: Carlos Molina

Generation: 2026-01-25T12:01:56.873Z