// ACM-ICPC‘“ΰ—\‘I2012 E. ½’†Œo˜H

#include <iostream>
#include <cstdio>
#include <vector>
#include <complex>

using namespace std;

const double EPS = 1e-10;

typedef complex<double> P;
typedef pair<P,double> circle;

struct L { P p, q; L(P p, P q) : p(p), q(q) {} };

double cross(P a, P b) { return imag(conj(a)*b); }

bool ssIntersect(L a, L b){
	if(abs(imag((a.q-a.p)/(b.q-b.p)))<EPS) return false;
	return cross(a.q-a.p, b.p-a.p)*cross(a.q-a.p, b.q-a.p) < 0 &&
    	   cross(b.q-b.p, a.p-b.p)*cross(b.q-b.p, a.q-b.p) < 0;
}

void crossPoint(vector<P> &res, circle c1, circle c2){
	double r1 = c1.second;
	double r2 = c2.second;
	double r3 = abs(c1.first-c2.first);
	double rc = (r3*r3+r1*r1-r2*r2)/(2*r3);
	double rs = sqrt(r1*r1-rc*rc);
	P dif = (c2.first-c1.first)/r3;
	res.push_back(c1.first+dif*P(rc, rs));
	res.push_back(c1.first+dif*P(rc,-rs));
}

int main(){
	int n;
	while(cin >> n, n){
		vector<circle> vc(n);
		for(int i=0;i<n;i++){
			int x, y, r; cin >> x >> y >> r;
			vc[i] = make_pair(P(x,y), r);
		}
		vector<P> vp;
		vp.push_back(vc[0].first);
		for(int i=0;i+1<n;i++) crossPoint(vp, vc[i], vc[i+1]);
		vp.push_back(vc.back().first);

		vector<double> dist(2*n, 1e12);
		dist[0] = 0;
		for(int i=0;i<2*n;i++){
			for(int j=i+1;j<2*n;j++){
				bool ok = true;
				for(int k=(i+1)/2+1;ok && k<(j+1)/2;k++)
					ok &= ssIntersect(L(vp[i], vp[j]), L(vp[2*k-1], vp[2*k]));
				if(ok) dist[j] = min(dist[j], dist[i]+abs(vp[i]-vp[j]));
			}
		}
		printf("%.8lf\n", dist[2*n-1]);
	}
}