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 SieveOfEratosthenes(n):
    c = []
    # Create a boolean array "prime[0..n]" and initialize
    #  all entries it as true. A value in prime[i] will
    # finally be false if i is Not a prime, else true.
    prime = [True for i in range(n+1)]
    p = 2
    while (p * p <= n):

        # If prime[p] is not changed, then it is a prime
        if (prime[p] == True):

            # Update all multiples of p
            for i in range(p * p, n+1, p):
                prime[i] = False
        p += 1

    # Print all prime numbers
    for p in range(2, n):
        if prime[p]:
            c.append(p)
    return c
d = {}
c = [pow(i,2) for i in SieveOfEratosthenes(1000000)]
for i in range(len(c)):
    d[c[i]]=1
n = int(input())
a = list(map(int,input().split()))
for i in range(len(a)):
    try:
        if(d[a[i]]==1):
            print('YES')
    except:
        print('NO')