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:
n = int(input()); L = [int(s) for s in input().split()];
#def isprime(m):
#   R = 0;
#    for i in range(2, int(m**0.5)+1):
#        if m % i == 0:
#            R = 1; break;
#    return 0 if R else 1;
##########################################TimeLimitExceeded
# To generate all the prime numbers under n,
# the main thing is the S.E. Algorithm!
# Then we do not need to use the "for for if % return".
#########################################The procedure:
# 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.
def SleveOfEratosthenes(SE):
    prime=[1 for i in range(SE+1)];
    p = 2;
    while(p*p<=SE):
        if prime[p]:
            # If prime[p] is not changed, then it is a prime
            # Update all multiples of p to be 0, not prime
            for i in range(2*p,SE+1,p):
                prime[i]=0;
        p += 1;
    prime[0]=prime[1]=0
    return prime
SElist = SleveOfEratosthenes(10**6)
for n in L:
    a = int(n**0.5)
    print("YES")if n==a**2 and SElist[a]else print("NO");