Perfect Number

The proper divisors of a number are its divisors other than the number itself. The proper divisors of 28 are 1, 2, 4, 7 and 14, and they add up to exactly 28. A number like that is called perfect.

Write is_perfect(n) that returns True if the positive integer n is perfect and False otherwise.

Examples

is_perfect(6)     # returns True     (1 + 2 + 3 = 6)
is_perfect(28)    # returns True
is_perfect(12)    # returns False    (1 + 2 + 3 + 4 + 6 = 16)

Constraints

• 1 <= n <= 1,000,000

Note

1 has no proper divisors, so their sum is 0 and 1 is not perfect.