You are given spheres in three-dimensional space by Evan. Each sphere is centered at and has a radius of . Two spheres intersect if there is a non-zero volume that overlaps. This means that two spheres that *touch* are not considered intersecting.

Out of the spheres, you want to choose a subset of spheres, such that the no pair of spheres intersect one other, and contains the most spheres.

How many spheres are in the largest subset?

#### Input Specification

The first line will contain the integer .

The next lines will each contain four integers, .

#### Output Specification

Output the size of the largest subset , such that no pair of spheres in the subset intersects one another.

#### Subtasks

##### Subtask 1 [20%]

##### Subtask 2 [10%]

##### Subtask 3 [20%]

##### Subtask 4 [50%]

No further constraints.

#### Sample Input 1

```
1
0 0 0 3
```

#### Sample Output 1

`1`

#### Explanation For Sample 1

You are given sphere centered at having a radius of . Of course, this sphere can be in the subset. Thus, the size of the largest subset is .

#### Sample Input 2

```
4
2 3 3 1
3 -5 10 3
0 0 0 5
4 3 0 1
```

#### Sample Output 2

`3`

#### Explanation For Sample 2

**Note that you do not need to pass this sample to pass some of the subtasks.**

The largest subset consists of selecting the first sphere, the second sphere, and the fourth sphere.

This can be seen from the image below:

The red sphere is the first sphere, the orange sphere is the second sphere, the blue sphere is the third sphere, and the green sphere is the fourth sphere.

## Comments