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:
'''
Created on May 11, 2015

@author: sshadmin
'''
p=[]
for i in range(2,1001):
    flag=True
    for j in range(2,i):
        if i % j==0:
            flag=False
            break
    if flag:
        p.append(i)
all=range(2,1000001)
for i in range(len(p)):
    tmp1=p[i]
    tmp=p[i]+tmp1
    while tmp<1000001:
        all[tmp-2]="X"
        tmp+=tmp1
all=set([x for x in all if x!="X" ])


n=input()
num=map(int,raw_input().strip().split())
for i in range(n):
    tmp=num[i]**0.5
    if tmp == int(tmp) and tmp in all:
        print "YES"
    else:
        print "NO"