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:
import math
n=int(input())
a=[int(x) for x in input().split()]
c=[0]*2000000
c[1]=1
ma=int(1000000)

for i in range(2,ma+1):
    if(c[i]==0):
        d=i
        for j in range(d*d,ma+1,i):
            c[j]=1

'''
for i in range(2,ma):
    if(i%6!=1 and i%6!=5):
        c[i]=1
        continue
    tmp=int(i**0.5)
    for j in range(5,tmp,6):
        if(i%j==0 or i%(j+2)==0):
            c[i]=1
            break
'''
for i in range(n):
    tmp=a[i]
    b=a[i]**0.5
    if(b==int(b)):
        if(c[int(b)]==0):
            print("YES")
        else:
            print("NO")
    else:
        print("NO")