2-variable Function

Given an integer $n$, find the smallest integer $x$ that satisfies two conditions:

• $x$ is greater than or equal to $n$;

• There is a pair of non-negative integers $(a,b)$ such that $x=a^3+a^2\cdot b+a\cdot b^2+b^3$.

Input

One nonnegative integer $n(n\le 10^{18})$.

Output

Print the smallest value of $x$.

Examples