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 PYTHON3):

Solution:
from math import sqrt
n=input() #useless input
n=list(map(int,input().split()))
#code
oo=1000000
p=[1]*(oo+1)
def getp():
    global p
    p[0]=p[1]=0
    for n in range(int(sqrt(oo))+1):
        if p[n]:
            j=n**2
            while 1:
                if j>oo:break
                p[j]=0
                j+=n
def issq(n):
    n=sqrt(n)
    if n==int(n):
        return 1
    return 0
getp()
for v in n:
    if issq(v) and p[int(sqrt(v))]:
        print('YES')
    else:
        print('NO')
getp()
#code