ModuloFourDivisor | Topcoder Archive

Problem Statement

A quadruplet of non-negative integers (a,b,c,d) is called a divisor quadruplet if there exists at least one positive integer N that satisfies the following four conditions:

N has exactly a divisors x such that x &equiv; 0 (mod 4).
N has exactly b divisors x such that x &equiv; 1 (mod 4).
N has exactly c divisors x such that x &equiv; 2 (mod 4).
N has exactly d divisors x such that x &equiv; 3 (mod 4).

You are given long[]s A, B, C and D. Return the number of divisor quadruplets (a,b,c,d) such that A contains a, B contains b, C contains c and D contains d.

Definition

Class:: ModuloFourDivisor
Method:: countQuadruplets
Parameters:: long[], long[], long[], long[]
Returns:: int
Method signature:: int countQuadruplets(long[] A, long[] B, long[] C, long[] D)
(be sure your method is public)

Notes

x &equiv; k (mod 4) means (x - k) is divisible by 4.

Constraints

A, B, C and D will contain between 1 and 50 integers, inclusive.
Each element of A, B, C and D will be between 0 and 1,000,000,000,000,000,000 (10^18), inclusive.
A, B, C and D will contain no duplicate elements.

Examples

```
{1}
```
```
{1}
```
```
{1}
```
```
{0}
```
```
Returns: 1
```
(1, 1, 1, 0) is a divisor quadruplet because N = 4 satisfies the conditions.
```
{0}
```
```
{0}
```
```
{0}
```
```
{0}
```
```
Returns: 0
```
All integers have at least one divisor.
```
{0}
```
```
{0,1}
```
```
{0}
```
```
{0}
```
```
Returns: 1
```
(0, 0, 0, 0) is not a divisor quadruplet. (0, 1, 0, 0) is a divisor quadruplet.

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