We know that prime numbers are positive integers that have exactly two distinct positive divisors. Similarly, we'll call a positive integer $*t*$ Т-prime, if $*t*$ has exactly three distinct positive divisors.

You are given an array of $*n*$ positive integers. For each of them determine whether it is Т-prime or not.

Input

The first line contains a single positive integer, $*n*$ ($1 ≤ *n* ≤ 10^{5}$), showing how many numbers are in the array. The next line contains $*n*$ space-separated integers $*x*_{*i*}$ ($1 ≤ *x*_{*i*} ≤ 10^{12}$).

Please, do not use the %lld specifier to read or write 64-bit integers in С++. It is advised to use the cin, cout streams or the %I64d specifier.

Output

Print $*n*$ lines: the $*i*$-th line should contain "YES" (without the quotes), if number $*x*_{*i*}$ is Т-prime, and "NO" (without the quotes), if it isn't.

Note

The given test has three numbers. The first number 4 has exactly three divisors — 1, 2 and 4, thus the answer for this number is "YES". The second number 5 has two divisors (1 and 5), and the third number 6 has four divisors (1, 2, 3, 6), hence the answer for them is "NO".