Practical numbers

A practical number is a natural $n$ such that all smaller naturals can be represented as sums of distinct divisors of $n$ . For instance, 12 is a practical number, because all numbers from 1 to 11 can be expressed as sums of 1, 2, 3, 4, and 6: $5 = 2 + 3$ , $7 = 1 + 6$ , $8 = 2 + 6$ , $9 = 3 + 6$ , $10 = 1 + 3 + 6$ , and $11 = 2 + 3 + 6$ .

Given several naturals, are them practical numbers?

Input

Input consists of at most 50 naturals, all between 1 and $10^6$ .

Output

For each given natural, print “yes” or “no” depending on whether it is a practical number or not.

Problem information

Author: Salvador Roura

Generation: 2026-01-25T11:42:44.543Z