Problem: 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 ≤ 105), showing how many numbers are in the array. The next line contains n space-separated integers xi (1 ≤ xi ≤ 1012).

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 xi is Т-prime, and "NO" (without the quotes), if it isn't.

Examples

Input

3
4 5 6


Output

YES
NO
NO

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".

Solution (in PYTHON):

Solution:
from math import sqrt
n = int( raw_input() )
L =map(int,raw_input().split())
N = 10**6+1
x = [0]*N
x[1] = 1
x[0] = 1
for i in xrange(2,N):
    if x[i] == 1:
        continue
    for j in xrange(2*i,N,i):
        x[j] = 1
res = []
for i in range(n):
    c = int( sqrt(L[i]) )
    if c**2 == L[i] and L[i] != 1:
        if x[c] == 0:
            res.append("YES")
        else:
            res.append("NO")
    else:
        res.append("NO")
    res.append("\n")
    
print "".join(res)