The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

Codeforces Round 142 (Div. 2) |
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Finished |

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binary search

implementation

math

number theory

*1300

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B. T-primes

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputWe 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* ≤ 10^{5}), showing how many numbers are in the array. The next line contains *n* space-separated integers *x*_{i} (1 ≤ *x*_{i} ≤ 10^{12}).

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 *x*_{i} 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".

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