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D - 2-variable Function

Score : $400$ points

Problem Statement

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 $X=a^3+a^2b+ab^2+b^3$.

Constraints

• $N$ is an integer.
• $0 \le N \le 10^{18}$

Input

Input is given from Standard Input in the following format:

$N$

Output

Print the answer as an integer.

9

15

For any integer $X$ such that $9 \le X \le 14$, there is no $(a, b)$ that satisfies the condition in the statement.
For $X=15$, $(a,b)=(2,1)$ satisfies the condition.

0

0

$N$ itself may satisfy the condition.

999999999989449206

1000000000000000000

Input and output may not fit into a $32$-bit integer type.