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(i) for i in input().split(' ')]
maxx=0
for i in a:
    if i>maxx:
        maxx=i
prost=[]
maxx=int((math.sqrt(maxx)))
for i in range(maxx+1):
    prost.append(i)
prost[0]=-1
if len(prost)>1:
    prost[1]=-1
for i in range(int(math.sqrt(maxx))+1):
    if prost[i]!=-1:
        for j in range(prost[i]*prost[i],maxx+1,prost[i]):
            prost[j]=-1
prost2=set([])
for i in prost:
    if i!=-1:
        prost2.add(i)
prost=prost2
for i in range(n):
    if math.sqrt(a[i]) in prost:
        print('YES')
    else:
        print('NO')