Setting

Our university has an unusually long corridor which, being underground, has to be lit. By lights. Now, here's the catch: in order to not make things easy on its employees, the university has decided to give each light its own switch to switch it on and off, placed at the corridor's wall next to the light. Due to this unfortunate decision, the employees have revolted until a dedicated light switcher was appointed.

The mighty light switcher is, alas, mighty mad as well and thus does a peculiar thing. Given \(n\) lights in the corridor, he walks down the corridor \(n\) times and, in the \(i\)-th walk, toggles only the switches whose rank is divisible by \(i\). When he reaches the end of the corridor, he comes back to the beginning without toggling any switches and starts the next walk.

If the lights are off at the beginning, what is the state of the last light after \(n\) walks?

Input

The input will be an integer indicating the number of lights \(n\), which is \(\leq 2^{32} - 1\). A zero indicates the end of input.

Output

For each test case, print yes or no on a separate line as the light is on or off, respectively.

Sample Input

3
6241
8191
0

Sample Output

no
yes
no

This challenge is provided by the ACM International Collegiate Programming Contest.

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Statistics

Difficulty (10 votes)
Average test runtime 0.26
Points (changes over time) 20
Tried by 56 users
Solved by 39 users

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