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:
def sieve(b):
        a=[0]*(b+1)
        p=[]
        for i in range(2,b+1):
                if a[i]==0:
                        p.append(i)
                for j in range(i,b+1,i):
                        a[j]=1
        return p

def check(t,x):
        if t==1:
                return 0
        if int(t)-t==0:
                if binarysearch(x,int(t))==1:
                        return 1
                else:
                        return 0
        else:
                #print(t)
                return 0
def binarysearch(x,a):
	i=0
	l=len(x)-1
	while(i<=l):
		mid=(i+l)//2
		if x[mid]==a:
			return 1
		elif x[mid]>a:
			l=mid-1
		else:
			i=mid+1
	return 0
        
n=int(input())
a=[float(i)**0.5  for i in input().split()]
b=int(max(a))
x=sieve(b)
for i in a:
        p=check(i,x)
        if p==1:
                print('YES')
        else:
                print('NO')