#include <fstream>
#include <iostream>
#include <set>
#include <climits>
#include <cassert>

using namespace std;

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

#define NSQUARE_MAX 1000

typedef unsigned long long ullong;

class Rational {
public:
	ullong n, d;

	Rational( ullong ng, ullong dg ) {
		const ullong g = gcd(ng, dg);
		n = ng/g;
		d = dg/g;
	}

	static Rational average( const Rational &a, const Rational &b ) {
		return Rational(a.n*b.d + b.n*a.d, 2*a.d*b.d);
	}

	bool operator < ( const Rational &r ) const { return (n*r.d < r.n*d); }
	bool operator == ( const Rational &r ) const { return (n == r.n && d == r.d); }

private:
	static ullong gcd( ullong m, ullong n ) { return (n == 0)? m : gcd(n, m%n); }

};

class Square {
public:
	int x, y, length;

	// 正方形と原点からの光との衝突をみるとなると (x, y+length), (x+length, y) を通る
	// 直線の y 切片 (x+y+length) がソート基準に使える.
	bool operator < ( const Square &s ) const { return (x+y+length < s.x+s.y+s.length); }
};


int nsquare;
Square S[NSQUARE_MAX];
bool visible[NSQUARE_MAX];

bool collision( const Rational &l, const Square &s ) {
	const Rational ymin = Rational(l.n*s.x, l.d);
	const Rational ymax = Rational(l.n*(s.x+s.length), l.d);
	const Rational yubound = Rational(s.y+s.length, 1);
	const Rational ylbound = Rational(s.y, 1);
	return (ymin < yubound && ylbound < ymax);
}

bool tangent( const Rational &l, const Square &s ) {
	const Rational ymin = Rational(l.n*s.x, l.d);
	const Rational ymax = Rational(l.n*(s.x+s.length), l.d);
	const Rational yubound = Rational(s.y+s.length, 1);
	const Rational ylbound = Rational(s.y, 1);
	return (ymin == yubound || ymax == ylbound);
}

void compute( const Rational &l1, const Rational &l2 ) {
	// l1 と l2 のどちらにも接するまたは衝突すれば見えている.
	for ( int i = 0; i < nsquare; i++ ) {
		const bool c1 = collision(l1, S[i]);
		const bool t1 = tangent(l1, S[i]);
		const bool c2 = collision(l2, S[i]);
		const bool t2 = tangent(l2, S[i]);
		if ( (c1||t1) && (c2||t2) ) visible[i] = true;
		if ( c1 || c2 ) break;
	}
}

int main() {
	while ( cin >> nsquare, nsquare ) {
		for ( int i = 0; i < nsquare; i++ ) cin >> S[i].x >> S[i].y >> S[i].length;
		sort(S, S+nsquare);

		set<Rational> RS;
		for ( int i = 0; i < nsquare; i++ ) {
			RS.insert(Rational(S[i].y+S[i].length, S[i].x));
			RS.insert(Rational(S[i].y, S[i].x+S[i].length));
		}

		for ( int i = 0; i < nsquare; i++ ) visible[i] = false;

		for ( set<Rational>::iterator curr = RS.begin(); curr != RS.end(); curr++ ) {
			set<Rational>::iterator prev = curr; prev--;
			set<Rational>::iterator next = curr; next++;
			if ( curr != RS.begin() ) compute(*curr, Rational::average(*curr, *prev));
			if ( next != RS.end() ) compute(*curr, Rational::average(*curr, *next));
		}

		int nvisible = 0;
		for ( int i = 0; i < nsquare; i++ )
			if ( visible[i] ) nvisible++;
		cout << nvisible << endl;
	}

	return 0;
}