Short Cube

Input

A single natural number, $k$.

Output

Output the smallest natural number (a strictly positive integer) whose cube is divisible by $k$ without leaving a remainder.

Examples

Note

For instance, neither 1^3 = 1, 2^3 = 8, 3^3 = 27, 4^3 = 64, nor 5^3 = 125 are divisible by 12 without a remainder. However, 6^3 = 216 is divisible by 12. Therefore, 6 is the smallest natural number whose cube is a multiple of 12.

Scoring

• 20% of the points are awarded for tests where 2 \le k \le 100.

• Another 20% of the points are for 10^5 \le k \le 10^6.

• Another 20% of the points are for 10^7 \le k \le 10^8.

• Another 20% of the points are for 10^{10} \le k \le 10^{12}.

• The remaining 20% of the points are for 10^{15} \le k \le 10^{18}.