# UVa 10110

## Summary

Figure out how many times Mabu toggles the $n$ th switch to figure out whether the switch is on or not.

## Explanation

There are a few things you should immediately notice:

• Once Mabu has done his $n$ th walk, the $n$ th switch is never toggled again.
• The answer is yes iff the $n$ th switch is toggled an odd number of times (otherwise, for each time it is turned on, it gets turned off, and is thus off in the end).
• The $n$ th switch is toggled once for each factor of $n$ .

With this in mind, how can we tell if a number has an even or odd number of factors? For every factor $n$ has below ${\sqrt {n}}$ it has one above ${\sqrt {n}}$ . This suggests that unless $n$ is a perfect square, it has an even number of factors. So, the problem boils down to deciding if $n$ is a perfect square or not. Use your favorite math libraries to find the answer.

## Implementation

• 31-bit integer is not good enough for this problem. Use unsigned int.

## Input

3
6241
8191
0


## Output

no
yes
no