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:
import sys
import math
def primes(limit):
    Ans=[]
    C=[True]*(limit+1)
    L=list(range(2,limit+1))
    for item in L:
        if(C[item]):
            i=2
            while(item*i<=limit):
                C[item*i]=False
                i+=1
    for item in L:
        if(C[item]):
            Ans+=[item]
    return Ans


N=int(sys.stdin.readline())

L=list(map(int,sys.stdin.readline().split()))
p=primes(1000000)

C=[False]*1000001
for item in p:
    C[item]=True
Ans=""

for item in L:
    x=int(math.sqrt(item))
    if(x*x==item and C[x]):
        Ans+="YES\n"
    else:
        Ans+="NO\n"
sys.stdout.write(Ans)