A Kitty Number N is a positive integer satisfies that given two any positive integers A and B, and among A, B and N, if we have
N | ((A^2)*B+1)
Then
N | (A^2+B)
Now, you are asked to judge a given positive number is Kitty Number or not.
The first line there is a number T (0 < T < 5000), denoting the test case number.
The following T lines for each line there is a positive number N (0 < N < 5000) you need to judge.
For each case, output “YES” if the given number is Kitty Number, “NO” if it is not.
X | Y means X is a factor of Y, for example 3 | 9;
X^2 means X multiplies itself, for example 3^2 = 9;
X*Y means X multiplies Y, for example 3*3 = 9.