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:
from math import sqrt
dict={}
from collections import defaultdict
dict=defaultdict(lambda:0,dict)
'''def Sqrt(x) :
    if (x == 0 or x == 1) :
        return x
    start = 1
    end = x
    while (start <= end) :
        mid = (start + end) // 2

        if (mid*mid == x) :
            return mid
        if (mid * mid < x) :
            start = mid + 1
            ans = mid

        else :
            end = mid-1
    return ans'''
'''def binary(t,low,high,x):
    if(low<=high):
        mid=(low+high)//2
        #print(t[mid])
        if t[mid]==x:
            return True
        elif t[mid]>x:
            return binary(t,low,mid-1,x)
        else:
            return binary(t,mid+1,high,x)
    else:
        return False'''
def SieveOfEratosthenes(n):
    prime = [True for i in range(n+1)]
    y=[]
    p = 2
    while (p * p <= n):
        if (prime[p] == True):
            for i in range(p * p, n+1, p):
                prime[i] = False
        p += 1
    for i in range(2,len(prime)):
        if prime[i]:
            y.append(i)

    return y
t=SieveOfEratosthenes(1000000)
for i in t:
    dict[i*i]=1
n=int(input())
a=[int(x) for x in input().split()]
for i in range(n):
    if dict[a[i]]==1:
        print('YES')
    else:
        print('NO')