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())
u = input()
list = [int(x) for x in u.split()]
def primes(n):
    arr = []
    f = []
    for i in range(n + 1):
        if i > 2 and i % 2 == 0:
            f.append(1)
        else:
            f.append(0)
    i = 3
    while i * i <= n:
        if f[i] == 0:
            j = i * i
            while j <= n:
                f[j] = 1
                j += i + i
        i += 2
    arr.append(4)
    for x in range(3, n + 1, 2):
        if f[x] == 0:
            arr.append(x**2)
    return arr
n = 1000000
arr = primes(n)
for x in list:
    def binarySearch(arr, l, r, x):
        if l <= r:
            mid = (l + r) // 2
            if arr[mid] == x:
                return mid
            elif arr[mid] > x:
                return binarySearch(arr, l, mid - 1, x)
            else:
                return binarySearch(arr, mid + 1, r, x)
        else:
            return -1
    result = binarySearch(arr, 0, len(arr) - 1, x)
    if result==-1:
        print("NO")
    else:
        print("YES")