EnclosingSquare | Topcoder Archive

Problem Statement

Find the area of the minimum square in the plane, such that its 4 vertices are distinct lattice points and there are exactly n lattice points strictly inside it. If there is no such square, return 0 instead.

Definition

Class:: EnclosingSquare
Method:: getMinimum
Parameters:: long
Returns:: long
Method signature:: long getMinimum(long n)
(be sure your method is public)

Notes

A lattice point in the coordinate plane is a point whose x-coordinate and y-coordinate are both integers.

Constraints

n will be between 0 and 1,000,000,000,000, inclusive.

Examples

```
4
```
```
Returns: 5
```
The square below contains exactly 4 lattice points strictly inside itself and has an area of 5.
```
3
```
```
Returns: 0
```
There is no such square.
```
1000000000000
```
```
Returns: 1000000000001
```
```
101
```
```
Returns: 104
```
```
85
```
```
Returns: 90
```

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