Firecrackers scare Nian the monster, but they're wayyyyy too noisy! Maybe fireworks make a nice complement.

Little Tommy is watching a firework show. As circular shapes spread across the sky, a splendid view unfolds on the night of Lunar New Year's eve.

A wonder strikes Tommy. How many regions are formed by the circles on the sky? We consider the sky as a flat plane. A region is a connected part of the plane with positive area, whose bound consists of parts of bounds of the circles and is a curve or several curves without self-intersections, and that does not contain any curve other than its boundaries. Note that exactly one of the regions extends infinitely.

Input

The first line of input contains one integer $*n*$ ($1 ≤ *n* ≤ 3$), denoting the number of circles.

The following $*n*$ lines each contains three space-separated integers $*x*$, $*y*$ and $*r*$ ($- 10 ≤ *x*, *y* ≤ 10$, $1 ≤ *r* ≤ 10$), describing a circle whose center is $(*x*, *y*)$ and the radius is $*r*$. No two circles have the same $*x*$, $*y*$ and $*r*$ at the same time.

Output

Print a single integer — the number of regions on the plane.

Note

For the first example,

For the second example,

For the third example,