#include <algorithm>
#include <cmath>
#include <iostream>
#include <fstream>
#include <set>
#include <vector>
using namespace std;

ifstream fin("squares.txt");
#define cin fin

struct Square {
    int x, y, l;
    double a, b; // 原点から {右下角, 左上角} を望んだ角度
};

double calc_dist_to_edge(Square &s, double angle)
{
    double middle_angle = atan2((double)s.y, (double)s.x);
    if (angle < middle_angle) // 右下半分
        return s.y / sin(angle);
    else
        return s.x / cos(angle);
}

int count_visible_squares(vector<Square> &squares)
{
    vector<double> angles;
    for (int i = 0; i < squares.size(); i++) {
        angles.push_back(squares[i].a);
        angles.push_back(squares[i].b);
    }
    sort(angles.begin(), angles.end());

    set<int> visible_squares;
    for (int i = 0; i < angles.size() - 1; i++) {
        if (angles[i+1] - angles[i] < 1e-8)
            continue;
        int visible_square = -1;
        double min_dist = 1e8;
        for (int j = 0; j < squares.size(); j++) {
            if (squares[j].a <= angles[i] && angles[i+1] <= squares[j].b) {
                double dist = calc_dist_to_edge(squares[j], angles[i]);
                if (dist < min_dist) {
                    visible_square = j;
                    min_dist = dist;
                }
            }
        }
        if (visible_square != -1)
            visible_squares.insert(visible_square);
    }

    return visible_squares.size();
}

int main()
{
    int n;
    while (cin >> n, n) {
        vector<Square> squares;
        for (int i = 0; i < n; i++) {
            Square s;
            cin >> s.x >> s.y >> s.l;
            s.a = atan2((double)s.y, (double)s.x+s.l);
            s.b = atan2((double)s.y+s.l, (double)s.x);
            squares.push_back(s);
        }
        cout << count_visible_squares(squares) << endl;
    }
    return 0;
}