CF859G.Circle of Numbers

$n$ evenly spaced points have been marked around the edge of a circle. There is a number written at each point. You choose a positive real number $k$ . Then you may repeatedly select a set of $2$ or more points which are evenly spaced, and either increase all numbers at points in the set by $k$ or decrease all numbers at points in the set by $k$ . You would like to eventually end up with all numbers equal to $0$ . Is it possible?

A set of $2$ points is considered evenly spaced if they are diametrically opposed, and a set of $3$ or more points is considered evenly spaced if they form a regular polygon.

The first line of input contains an integer $n$ ( $3<=n<=100000$ ), the number of points along the circle.

The following line contains a string $s$ with exactly $n$ digits, indicating the numbers initially present at each of the points, in clockwise order.

Print "YES" (without quotes) if there is some sequence of operations that results in all numbers being $0$ , otherwise "NO" (without quotes).

You can print each letter in any case (upper or lower).

If we label the points from $1$ to $n$ , then for the first test case we can set $k=1$ . Then we increase the numbers at points $7$ and $22$ by $1$ , then decrease the numbers at points $7$ , $17$ , and $27$ by $1$ , then decrease the numbers at points $4$ , $10$ , $16$ , $22$ , and $28$ by $1$ .