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:
prime=[]
prime2=[]
def seive(a):
    for i in range(2,a+1):
        for j in range(2,int(i**(0.5))+1):
            if i%j==0:
                break
        else:
            prime2.append(i)
def segmented():
    seive(1000)
    a=[0 for i in range(10**6+1)]
    for i in prime2:
        for j in range(i*i,10**6+1,i):
            a[j]=1
    for i in range(2,10**6+1):
        if a[i]==0:
            prime.append(i)
segmented()
prime.append(10**9)
from sys import stdin,stdout
n=int(stdin.readline())
a=[int(i) for i in stdin.readline().split()]
from bisect import bisect_left
for i in range(n):
    x=a[i]**(0.5)
    if int(x)==x and x>1:
        x=int(x)
        if prime[bisect_left(prime,x)]==x:
            stdout.write("YES \n")
            continue
    stdout.write("NO \n")