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.

Input

Input is given from Standard Input in the following format:
N

Output

Print the answer as an integer.

Constraints

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

Sample Input 1

9

Sample Output 1

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.

Sample Input 2

0

Sample Output 2

0

N itself may satisfy the condition.

Sample Input 3

999999999989449206

Sample Output 3

1000000000000000000

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

见题面 Input 部分

见题面 Output 部分