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:
#stdin.readline()
#int(stdin.readline())
#stdout.write()
#raw_input()
#map(int,raw_input().split())
#map(int,stdin.readline().split())
def main():
    n=pow(10,6)+1
    f=[True]*n
    f[0]=f[1]=False
    t=int(pow(n,0.5))+1
    for i in xrange(2,t):
        if f[i]:
            for j in xrange(i*i,n,i):
                f[j]=False
    n=input()
    a=map(int,stdin.readline().split())
    for i in a:
        if i==1:
            print "NO"
        else:
            t=int(pow(i,0.5))
            if t*t==i and f[t]:
                print "YES"
            else:
                print "NO"
if __name__ == "__main__":
    from sys import stdin, stdout
    main()