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 bin_search(l, n, item):
    first = 0
    last = n - 1
    while first <= last:
        mid = (first + last) // 2
        if l[mid] == item:
            return True
        elif item > l[mid]:
            first = mid + 1
        else:
            last = mid - 1
    return False

MAX = 1000005
arr = [True for i in range(MAX + 1)]

p = 2
while p <= MAX:
    if arr[p]:
        for i in range(p * p, MAX, p):
            arr[i] = False
    p += 1

sqr = []
for i in range(2, MAX + 1):
    if arr[i]:
        sqr.append(i * i)

len_sqr = len(sqr)

n = int(input())
inp = list(map(int, input().split()))

for i in inp:
    if bin_search(sqr, len_sqr, i):
        print("YES")
    else:
        print("NO")