The number n is called a degree number if its possible to get it from some other number multiplying itself with at least one time. For example 4 is a degree number because 4 = 2 · 2, 27 is also the degree number because 27 = 3 · 3 · 3, 28 is not a degree number. You are given numbers. Are they degree numbers?

Input

The first line contains the number n (1 ≤ n ≤ 10).The second line contains n integers, each greater than 1 and less than 109.

Output

Print n lines. Print in the i-th line YES, if the i-th number is a degree number and NO otherwise.