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 PYTHON):

Solution:
import math

def binarySearch(arr, ele):
	l, r  = 0, len(arr) -1
	while l <= r:
		mid = (l+r)/2
		# print("searching for mid ", mid)
		if arr[mid] == ele:
			return 1
		elif arr[mid] < ele:
			l = mid +1
		elif arr[mid] > ele:
			r = mid -1
	# print("not found")
	return -1

a= 10**6
unmarked =[]
for i in range(a+1):
	unmarked.append(False)
for i in range(2):
	unmarked[i] = True
prime = [] 
for i in range(2, int(math.sqrt(a))+1):
	if not unmarked[i]:
		for g in range(i*i, a+1, i):
			unmarked[g] = True
# for i in range(len(unmarked)):
# 	if not unmarked[i]:
# 		prime.append(i*i)
no = raw_input()
arr = map(int,raw_input().split())
# finalArr = []
# a = []
# # for i in range(100):
# # 	a.append(i)
# # found = binarySearch(a, 101)
# # print("found array is ", found)
# for i in arr:
# 	found = binarySearch(prime, long(i))
# 	if(found == 1):
# 		print("YES")
# 	else:
# 		print("NO")

for i in arr:
	no = int(math.sqrt(i))
	if(not unmarked[no] and no*no == i):
		print("YES")
	else:
		print("NO")