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 sys
import string
import math
import heapq
from collections import defaultdict
from collections import deque
from collections import Counter
from functools import lru_cache
from fractions import Fraction


def mi(s):
    return map(int, s.strip().split())

def lmi(s):
    return list(mi(s))

def tmi(s):
    return tuple(mi(s))

def mf(f, s):
    return map(f, s)

def lmf(f, s):
    return list(mf(f, s))

def js(lst):
    return " ".join(str(d) for d in lst)

def jsns(lst):
    return "".join(str(d) for d in lst)

def line():
    return sys.stdin.readline().strip()

def linesp():
    return line().split()

def iline():
    return int(line())

def mat(n):
    matr = []
    for _ in range(n):
        matr.append(linesp())
    return matr

def matns(n):
    mat = []
    for _ in range(n):
        mat.append([c for c in line()])
    return mat

def mati(n):
    mat = []
    for _ in range(n):
        mat.append(lmi(line()))
    return mat

def pmat(mat):
    for row in mat:
        print(js(row))

def prime(n):
    primes = [True for _ in range(n + 1)]
    primes[0] = False
    primes[1] = False

    for i in range(2, n + 1):
        if i * i > n:
            break

        if primes[i]:
            for j in range(i * i, n + 1, i):
                primes[j] = False

    return primes

def main():
    n = iline()
    arr = lmi(line())
    pp = prime(int(1e6 + 2))
    ans = set(i * i for i in range(len(pp)) if pp[i])
    for n in arr:
        if n in ans:
            print("YES")
        else:
            print("NO")

main()