Problem Description

Xiao Yang has a positive integer \( n \). He wants to know if \( n \) is a cubic number. A positive integer \( n \) is a cubic number if and only if there exists a positive integer \( x \) such that \( x \times x \times x = n \).

Input Format

The first line contains a positive integer \( n \).

Output Format

If the positive integer \( n \) is a cubic number, output Yes; otherwise, output No.

Sample Input and Output

Sample Input #1

8

Sample Output #1

Yes

Sample Input #2

9

Sample Output #2

No

Notes

For Sample 1, there exists a positive integer \( 2 \) such that \( 8 = 2 \times 2 \times 2 \), hence \( 8 \) is a cubic number.

For Sample 2, there is no positive integer that satisfies the condition, hence \( 9 \) is not a cubic number.

For all data, it is guaranteed that \( 1 \le n \le 1000 \).

见题面 Input 部分

见题面 Output 部分