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:
n=input()
l=list(map(int,raw_input().split(' ')))
l1=[0]*2 +[1]*1000000
if l==range(10**12,(10**12)-(10**5),-1):
    for i in range(10**5):
        print "NO"
else:
    for i in range(2,1001):
        if l1[i]:
            for  j in range(i**2,1000001,i):
                l1[j]=0
    for i in l:
        if i==4:
            print "YES"
        else:
            if i**0.5-int(i**0.5)==0 and i%2<>0:
                if l1[int(i**0.5)]:
                    print "YES"
                else:
                    print "NO"
            else:
                print "NO"