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:
line = int(input())
n = [int(x) for x in input().split()]

def primelist(x):
    l_all=[True for i in range(x+1)]
    l_all[0]=False
    l_all[1]=False
    l2=list(range(2,int(x**0.5)+2))
    for i in l2:
        if l_all[i]==True:
            for j in range(i*i,x+1,i):
                l_all[j]=False
    return l_all

l=primelist(10**6+1)

for i in n:
    if i**0.5==int(i**0.5) and l[int(i**0.5)]:
        print('YES')
    else:
        print('NO')