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.
The first line contains a single positive integer, *n* (1 ≤ *n* ≤ 10<sup class="upper-index">5</sup>), showing how many numbers are in the array. The next line contains *n* space-separated integers *x*<sub class="lower-index">*i*</sub> (1 ≤ *x*<sub class="lower-index">*i*</sub> ≤ 10<sup class="upper-index">12</sup>).

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.
import math

# Function to generate primes up to a given limit using Sieve of Eratosthenes
def sieve_of_eratosthenes(limit):
    is_prime = [True] * (limit + 1)
    is_prime[0] = is_prime[1] = False
    primes = []

    for p in range(2, int(math.sqrt(limit)) + 1):
        if is_prime[p]:
            for i in range(p * p, limit + 1, p):
                is_prime[i] = False

    for p in range(2, limit + 1):
        if is_prime[p]:
            primes.append(p)

    return primes

# Read the number of integers in the array
n = int(input())

# Read the array of integers
integers = list(map(int, input().split()))

# Generate a list of primes up to the square root of the maximum integer in the array
max_integer = max(integers)
primes = sieve_of_eratosthenes(int(math.sqrt(max_integer)))

# Check if each integer is Т-prime
for t in integers:
    sqrt_t = int(math.sqrt(t))
    if sqrt_t * sqrt_t == t and sqrt_t in primes:
        print("YES")
    else:
        print("NO")
