CF933C.A Colourful Prospect

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.

鞭炮能吓跑年兽，但它们实在太吵啦！或许烟花可以作为不错的补充。

小汤米正在观看一场烟花表演。当一个个圆形图案在夜空中扩散开来时，农历除夕之夜呈现出一幅壮丽的景象。

一个奇妙的问题突然闪现在汤米脑海中：这些圆在天空（即平面）上一共划分出了多少个区域？我们把天空视为一个平面。所谓“区域”，是指平面上具有正面积的一个连通部分，其边界由若干圆的边界弧段组成，且该边界是一条或若干条无自交的曲线；此外，该区域内部不包含除自身边界外的任何其他曲线。注意：恰好有一个区域是无限延伸的。

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.

输入的第一行包含一个整数 $n$（$1 \leq n \leq 3$），表示圆的个数。

接下来的 $n$ 行，每行包含三个用空格分隔的整数 $x$、$y$ 和 $r$（$-10 \leq x, y \leq 10$，$1 \leq r \leq 10$），描述一个圆心为 $(x, y)$、半径为 $r$ 的圆。任意两个圆不会同时具有相同的 $x$、$y$ 和 $r$。

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

输出一个整数——平面上的区域数量。

For the first example,

For the second example,

For the third example,

对于第一个例子，

对于第二个例子，

对于第三个例子，