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:
# import math
#
# def totDivisors(n, a, b):
#     res = 0
#     for i in range(1, int(math.sqrt(n))+1):
#         if b%i == 0 and a%i == 0:
#             res += 1
#             if not(i==b/i) and not(i==a/i) and a%(n/i)==0 and b%(n/i)==0:
#                 res+=1
#
#     return res
#
# t = int(input())
# for _ in range(t):
#     li = list(map(int, input().split()))
#     print(totDivisors(max(li), li[0], li[1]))


import math
def getPrimes():
    n = 10**6+1
    seive = [0]*(n+1)
    # 0 and 1 are not primes
    seive[0] = 1
    seive[1] = 1

    for i in range(2, int(math.sqrt(n))+1):
        if seive[i] == 0:
            for j in range(i, n+1):
                if j*i>n:
                    break
                else:
                    if seive[i*j]==0:
                        seive[i*j] = 1
    return seive

n = int(input())
li = list(map(int, input().split()))
totPrimes = getPrimes()
for i in range(n):
    temp = int(math.sqrt(li[i]))
    if totPrimes[temp] == 0 and temp*temp==li[i]:
        print("YES")
    else:
        print("NO")