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:
#!/usr/bin/pypy3

from sys import stdin,stderr

def readInts(): return map(int,stdin.readline().strip().split())
def print_err(*args,**kwargs): print(*args,file=stderr,**kwargs)
    
def solve(vs):
    return None

def tprimes():
    ps = [ True for _ in range(10**6+1) ]
    for pt in range(4,10**6+1,2): ps[pt] = False
    ps[0] = False
    ps[1] = False
    for pt in range(3,10**6+1):
        if pt*pt > 10**6: break
        if not ps[pt]: continue
        ptx = 3*pt
        while ptx <= 10**6:
            ps[ptx] = False
            ptx += 2*pt
    tps = set( p*p for p in range(10**6+1) if ps[p] )
    return tps
def run():    
    n, = readInts()
    tps = tprimes()
    for v in readInts():
        if v in tps: print("YES")
        else: print("NO")
        
run()