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.

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.

Examples

Input

3 0 0 1 2 0 1 4 0 1

Output

4

Input

3 0 0 2 3 0 2 6 0 2

Output

6

Input

3 0 0 2 2 0 2 1 1 2

Output

8

Note

For the first example,

For the second example,

For the third example,

inputFormat

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.

outputFormat

Output

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

Examples

Input

3 0 0 1 2 0 1 4 0 1

Output

4

Input

3 0 0 2 3 0 2 6 0 2

Output

6

Input

3 0 0 2 2 0 2 1 1 2

Output

8

Note

For the first example,

For the second example,

For the third example,

样例

3
0 0 2
3 0 2
6 0 2

6

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