9604: ABC246 —— D - 2-variable Function
[Creator : ]
Description
Given an integer $N$, find the smallest integer $X$ that satisfies all of the conditions below.
- $X$ is greater than or equal to $N$.
- There is a pair of non-negative integers $(a, b)$ such that $X=a^3+a^2b+ab^2+b^3$.
- $X$ is greater than or equal to $N$.
- There is a pair of non-negative integers $(a, b)$ such that $X=a^3+a^2b+ab^2+b^3$.
Input
Input is given from Standard Input in the following format:
```
$N$
```
```
$N$
```
Output
Print the answer as an integer.
Constraints
- $N$ is an integer.
- $0 \le N \le 10^{18}$
- $0 \le N \le 10^{18}$
Sample 1 Input
9
Sample 1 Output
15
For any integer X such that 9≤X≤14, there is no (a,b) that satisfies the condition in the statement.
For X=15, (a,b)=(2,1) satisfies the condition.
For X=15, (a,b)=(2,1) satisfies the condition.
Sample 2 Input
0
Sample 2 Output
0
N itself may satisfy the condition.
Sample 3 Input
999999999989449206
Sample 3 Output
1000000000000000000