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Ural SU contest. Petrozavodsk training camp. Winter 2008

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F. Dean's Financial Pyramid

Time limit: 0.5 second
Memory limit: 64 MB
The Dean of the Sports Programming Department in the Yekaterinozavosk State University was feeling strange. A team of the department had won an honourable right of the tourist trip to Canada. On the other hand, the Yekaterinozavodsk State University never paid money to students for their trips. The Dean decided to use crowdfunding to solve this problem. Thus, on December, 1 he called a famous sixth-year Student and asked him to write the request for financial support in the accounts department of the university (and promised to take him to Canada as a co-coach). Next day the Student had to convince some of his friends to visit the accounts department and write same kind of requests. During each of the following days the Student with the help of his friends had to find some other students and lead them to the accounts department. All of students' requests were stored in the accounts department.
However, the accounts department paid money only on even days of the month. Moreover, the Head Accountant agreed to pay the money only if at the end of some day there is exactly N requests on his table (this should be at the day of the payment). The financial support is paid simultaneously to all students who filed their requests. If N is large enough, the money obtained by the students would be enough to send to Canada the team with the coach, the Student and even the Dean, who invented this scheme.
Of course, the Student can influence the number of students writing the requests for financial support. However, he knows that in any case the total number of written requests will increase in the integral number of times (which may be different each day). What is more, somehow this number is either 2, or an odd number, greater than 1.


The first line contains an integer T — the number of test cases (1 ≤ T ≤ 100). Each of the following T lines contains an integer N (1 ≤ N ≤ 225 − 1).


For each of the test cases output “YES” if the Student can receive the money and “NO” in the other case.




In the first case the Student can make the number of requests equal to 4 only at the end of the third day (there will be 1 request at the end of the first day, and 2 at the end of the second day). But December, 3rd is an odd day, so the money won't be paid. In the second case there will be 1 request at the end of the first day and 7 at the end of the second day. In the fourth case the Student should first increase the number of requests in 2 times, then in 3 times, then in 5 times, resulting in 30 requests at the end of December, 4th.
Problem Author: Alex Samsonov
Problem Source: Ural SU Contest. Petrozavodsk Winter Session, January 2008
To submit the solution for this problem go to the Problem set: 1665. Dean's Financial Pyramid