Once, Beremiz explained to a sheikh what are perfect numbers: those whose sum of positive divisors, the number excluded, equals the number itself.

For instance, 6 is perfect, because all its positive divisors (except 6 itself) are 1, 2 and 3, and 1 + 2 + 3 = 6. Other perfect numbers are 28 and 496.

**Input**

Input consists of several natural numbers *n*,
all between 1 and 10^{12}.

**Output**

For every *n*, print the difference in absolute value
between the sum of the divisors of *n* (*n* excluded), and *n*.
Note that we can interpret this difference
as the “imperfection” of the number,
which is 0 only for perfect numbers.

**Observation**

At the time of the creation of this problem (year 2013), only 48 perfect numbers are known, all even. The largest one has about 35 million digits. It is unknown whether there are infinitely many perfect numbers, or if any of them is odd.

Public test cases

**Input**

6 5 100 496 497 1 1000000000000 999962000357 999999999989

**Output**

0 4 17 0 418 1 499694822171 999960000394 999999999988

Information

- Author
- Salvador Roura
- Language
- English
- Translator
- Salvador Roura
- Original language
- Spanish
- Other languages
- Spanish
- Official solutions
- C++
- User solutions
- C++