Complete Stars

Fernando got a compass for his birthday, and his favorite pastime now is drawing stars. He first marks $N$ points on a circle, splitting it into $N$ arcs of equal length. He then draws a segment from one point to the $k$-th point clockwise from it, and keeps drawing segments the same way until he returns to the starting point.

Depending on $k$, the drawing passes through every marked point or through only some of them. A star that passes through every point is called complete. For example, when $N = 8$ the four stars below can be drawn. Stars (a) and (c) are complete, while stars (b) and (d) are not.

The step $k$ is chosen in the range $1 \le k < N$, and $k$ and $N - k$ produce the same drawing, so they count as one star.

Given $N$, write a program that determines how many complete stars Fernando can draw.

The input consists of several test cases. Each line holds a single integer $N$, the number of arcs the circle was split into. The input continues until end of file.

Constraints

• $3 \le N < 2^{31}$

For each test case, print a single integer on its own line, the number of complete stars that can be drawn.