Given a number n, find if its 2nd, 4th and 8th roots are all integers (perfect roots), return true if it exists, false if not.

Examples

perfect_roots(256) ➞ true
# 2nd root of 256 is 16
# 4th root of 256 is 4
# 8th root of 256 is 2

perfect_roots(1000) ➞ false

perfect_roots(6561) ➞ true

Notes

n > 1