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 JAVA):

Solution:
var N = 1e6 + 5;
var p = new Int8Array( N );

p[0] = p[1] = 1;

for( var j = 2; j*2 < N; j++ )
	p[ j*2 ] = 1;

for( var i = 3; i < N; i+=2 )
	if( !p[i] )
		for( var j = 2; j*i < N; j++ )
			p[ j*i ] = 1;


readline();
var ret = readline()
			.split(' ')
			.map(Math.sqrt)
			.map(function(v){
				return v%1===0&&p[v]===0 ? 'YES' : 'NO';
			});

print(ret.join('\n'));