#include <bits/stdc++.h>

#define REP(i, n) for (int i = 0; i < (int)(n); i++)
#define ALL(x) (x).begin(), (x).end()

using namespace std;

typedef long double ld;
typedef complex<ld> Point;

const ld eps = 1e-9, pi = acos(-1.0);

namespace std {
bool operator<(const Point &lhs, const Point &rhs) {
  if (lhs.real() < rhs.real() - eps) return true;
  if (lhs.real() > rhs.real() + eps) return false;
  return lhs.imag() < rhs.imag();
}
}  // namespace std

Point input_point() {
  ld x, y;
  cin >> x >> y;
  return Point(x, y);
}

bool eq(ld a, ld b) { return (abs(a - b) < eps); }
//内積
ld dot(Point a, Point b) { return real(conj(a) * b); }
//外積
ld cross(Point a, Point b) { return imag(conj(a) * b); }

class Line {
 public:
  Point a, b;
  Line() : a(Point(0, 0)), b(Point(0, 0)) {}
  Line(Point a, Point b) : a(a), b(b) {}
};

class Circle {
 public:
  Point p;
  ld r;
  Circle() : p(Point(0, 0)), r(0) {}
  Circle(Point p, ld r) : p(p), r(r) {}
};
// 3点の位置関係
int ccw(Point a, Point b, Point c) {
  b -= a;
  c -= a;
  if (cross(b, c) > eps) return 1;    // a,b,cで反時計周り
  if (cross(b, c) < -eps) return -1;  // a,b,cで時計周り
  if (dot(b, c) < 0) return 2;        // c,a,bで直線
  if (norm(b) < norm(c)) return -2;   // a,b,cで直線
  return 0;                           // a,c,bで直線
}

bool isis_ll(Line l, Line m) { return !eq(cross(l.b - l.a, m.b - m.a), 0); }

bool isis_ls(Line l, Line s) {
  return isis_ll(l, s) &&
         (cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < eps);
}

bool isis_ss(Line s, Line t) {
  return ccw(s.a, s.b, t.a) * ccw(s.a, s.b, t.b) <= 0 &&
         ccw(t.a, t.b, s.a) * ccw(t.a, t.b, s.b) <= 0;
}

bool isis_lp(Line l, Point p) { return (abs(cross(l.b - p, l.a - p)) < eps); }

bool isis_sp(Line s, Point p) {
  return (abs(s.a - p) + abs(s.b - p) - abs(s.b - s.a) < eps);
}

Point proj(Line l, Point p) {
  ld t = dot(p - l.a, l.a - l.b) / norm(l.a - l.b);
  return l.a + t * (l.a - l.b);
}

Point is_ll(Line s, Line t) {
  Point sv = s.b - s.a, tv = t.b - t.a;
  assert(cross(sv, tv) != 0);
  return s.a + sv * cross(tv, t.a - s.a) / cross(tv, sv);
}

ld dist_lp(Line l, Point p) { return abs(p - proj(l, p)); }

ld dist_ll(Line l, Line m) { return isis_ll(l, m) ? 0 : dist_lp(l, m.a); }

ld dist_ls(Line l, Line s) {
  return isis_ls(l, s) ? 0 : min(dist_lp(l, s.a), dist_lp(l, s.b));
}

ld dist_sp(Line s, Point p) {
  Point r = proj(s, p);
  return isis_sp(s, r) ? abs(r - p) : min(abs(s.a - p), abs(s.b - p));
}

ld dist_ss(Line s, Line t) {
  if (isis_ss(s, t)) return 0;
  return min(
      {dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b)});
}

vector<Point> is_cc(Circle c1, Circle c2) {
  vector<Point> res;
  ld d = abs(c1.p - c2.p);
  ld rc = (d * d + c1.r * c1.r - c2.r * c2.r) / (2 * d);
  ld dfr = c1.r * c1.r - rc * rc;
  if (abs(dfr) < eps)
    dfr = 0.0;
  else if (dfr < 0.0)
    return res;
  ld rs = sqrt(dfr);
  Point diff = (c2.p - c1.p) / d;
  res.push_back(c1.p + diff * Point(rc, rs));
  if (dfr != 0.0) res.push_back(c1.p + diff * Point(rc, -rs));
  return res;
}

vector<Point> is_lc(Circle c, Line l) {
  vector<Point> res;
  ld d = dist_lp(l, c.p);
  if (d < c.r + eps) {
    ld len = (d > c.r) ? 0.0 : sqrt(c.r * c.r - d * d);
    Point nor = (l.a - l.b) / abs(l.a - l.b);
    res.push_back(proj(l, c.p) + len * nor);
    res.push_back(proj(l, c.p) - len * nor);
  }
  return res;
}

vector<Point> is_sc(Circle c, Line l) {
  vector<Point> v = is_lc(c, l), res;
  for (Point p : v)
    if (isis_sp(l, p)) res.push_back(p);
  return res;
}

vector<Line> tangent_cp(Circle c, Point p) {
  vector<Line> ret;
  Point v = c.p - p;
  ld d = abs(v);
  ld l = sqrt(norm(v) - c.r * c.r);
  if (isnan(l)) {
    return ret;
  }
  Point v1 = v * Point(l / d, c.r / d);
  Point v2 = v * Point(l / d, -c.r / d);
  ret.push_back(Line(p, p + v1));
  if (l < eps) return ret;
  ret.push_back(Line(p, p + v2));
  return ret;
}

vector<Line> tangent_cc(Circle c1, Circle c2) {
  vector<Line> ret;
  if (abs(c1.p - c2.p) - (c1.r + c2.r) > -eps) {
    Point center = (c1.p * c2.r + c2.p * c1.r) / (c1.r + c2.r);
    ret = tangent_cp(c1, center);
  }
  if (abs(c1.r - c2.r) > eps) {
    Point out = (-c1.p * c2.r + c2.p * c1.r) / (c1.r - c2.r);
    vector<Line> nret = tangent_cp(c1, out);
    ret.insert(ret.end(), ALL(nret));
  } else {
    Point v = c2.p - c1.p;
    v /= abs(v);
    Point q1 = c1.p + v * Point(0, 1) * c1.r;
    Point q2 = c1.p + v * Point(0, -1) * c1.r;
    ret.push_back(Line(q1, q1 + v));
    ret.push_back(Line(q2, q2 + v));
  }
  return ret;
}

typedef vector<Point> Polygon;

ld area(const Polygon &p) {
  ld res = 0;
  int n = p.size();
  REP(j, n) res += cross(p[j], p[(j + 1) % n]);
  return res / 2;
}

bool is_counter_clockwise(const Polygon &poly) {
  ld angle = 0;
  int n = poly.size();
  REP(i, n) {
    Point a = poly[i], b = poly[(i + 1) % n], c = poly[(i + 2) % n];
    angle += arg((c - b) / (b - a));
  }
  return angle > eps;
}

int is_in_polygon(const Polygon &poly, Point p) {
  ld angle = 0;
  int n = poly.size();
  REP(i, n) {
    Point a = poly[i], b = poly[(i + 1) % n];
    if (isis_sp(Line(a, b), p)) return 1;
    angle += arg((b - p) / (a - p));
  }
  return eq(angle, 0) ? 0 : 2;
}

Polygon convex_hull(vector<Point> ps) {
  int n = ps.size();
  int k = 0;
  sort(ps.begin(), ps.end());
  Polygon ch(2 * n);
  for (int i = 0; i < n; ch[k++] = ps[i++])
    while (k >= 2 && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
  for (int i = n - 2, t = k + 1; i >= 0; ch[k++] = ps[i--])
    while (k >= t && ccw(ch[k - 2], ch[k - 1], ps[i]) <= 0) --k;
  ch.resize(k - 1);
  return ch;
}

Polygon convex_cut(const Polygon &ps, Line l) {
  int n = ps.size();
  Polygon Q;
  REP(i, n) {
    Point A = ps[i], B = ps[(i + 1) % n];
    Line m = Line(A, B);
    if (ccw(l.a, l.b, A) != -1) Q.push_back(A);
    if (ccw(l.a, l.b, A) * ccw(l.a, l.b, B) < 0 && isis_ll(l, m))
      Q.push_back(is_ll(l, m));
  }
  return Q;
}

void add_point(vector<Point> &ps, Point p) {
  for (Point q : ps)
    if (abs(q - p) < eps) return;
  ps.push_back(p);
}

typedef int Weight;

struct Edge {
  int from, to;
  Weight weight;
};

typedef vector<Edge> Edges;
typedef vector<Edges> Graph;

void add_edge(Graph &g, int from, int to, Weight weight) {
  g[from].push_back((Edge){from, to, weight});
}

Graph segment_arrangement(const vector<Line> &s, const vector<Point> &p) {
  int n = p.size(), m = s.size();
  Graph g(n);
  REP(i, m) {
    vector<pair<ld, int>> vec;
    REP(j, n) if (isis_sp(s[i], p[j])) vec.emplace_back(abs(s[i].a - p[j]), j);
    sort(ALL(vec));
    REP(j, vec.size() - 1) {
      int from = vec[j].second, to = vec[j + 1].second;
      add_edge(g, from, to, abs(p[from] - p[to]));
    }
  }
  return g;
}

Graph circle_arrangement(const vector<Circle> &c, const vector<Point> &p) {
  int n = p.size(), m = c.size();
  Graph g(n);
  REP(i, m) {
    vector<pair<ld, int>> vec;
    REP(j, n)
    if (abs(abs(c[i].p - p[j]) - c[i].r) < eps)
      vec.emplace_back(arg(c[i].p - p[j]), j);
    sort(ALL(vec));
    REP(j, vec.size() - 1) {
      int from = vec[j].second, to = vec[j + 1].second;
      ld angle = vec[j + 1].first - vec[j].first;
      add_edge(g, from, to, angle * c[i].r);
    }
    if (vec.size() >= 2) {
      int from = vec.back().second, to = vec.front().first;
      ld angle = vec.front().first - vec.back().first;
      add_edge(g, from, to, angle * c[i].r);
    }
  }
  return g;
}

vector<vector<int>> polygon;
vector<int> seg2p[1024][1024];

Graph dual_graph(const vector<Line> &s, const vector<Point> &p) {
  int N = p.size();
  polygon.clear();
  REP(i, 1024) REP(j, 1024) seg2p[i][j].clear();
  vector<vector<tuple<ld, int, bool>>> tup(N);
  REP(i, s.size()) {
    int a = -1, b = -1;
    REP(j, N) if (abs(s[i].a - p[j]) < eps) a = j;
    REP(j, N) if (abs(s[i].b - p[j]) < eps) b = j;
    assert(a >= 0 && b >= 0);
    tup[a].emplace_back(arg(s[i].b - s[i].a), b, false);
    tup[b].emplace_back(arg(s[i].a - s[i].b), a, false);
  }
  REP(i, N) sort(ALL(tup[i]));
  REP(i, N) {
    REP(j, tup[i].size()) {
      ld angle;
      int pos = j, from = i, to;
      bool flag;
      tie(angle, to, flag) = tup[i][j];
      if (flag) continue;
      vector<int> ps;
      while (!flag) {
        ps.push_back(from);
        get<2>(tup[from][pos]) = true;
        seg2p[from][to].push_back(polygon.size());
        seg2p[to][from].push_back(polygon.size());
        angle += pi + eps;
        if (angle > pi) angle -= 2 * pi;
        auto it = lower_bound(ALL(tup[to]), make_tuple(angle, 0, false));
        if (it == tup[to].end()) it = tup[to].begin();
        from = to;
        tie(angle, to, flag) = *it;
        pos = it - tup[from].begin();
      }
      polygon.push_back(ps);
    }
  }
  Graph g(polygon.size());
  REP(i, N) REP(j, i) {
    if (seg2p[i][j].size() == 2) {
      int from = seg2p[i][j][0], to = seg2p[i][j][1];
      g[from].push_back((Edge){from, to});
      g[to].push_back((Edge){to, from});
    }
  }
  return g;
}

const ld zoom = 25;
const ld centerX = 6;
const ld centerY = 5;

void change_color(int r, int g, int b) {
  fprintf(stderr, "c.strokeStyle = 'rgb(%d, %d, %d)';\n", r, g, b);
}

int cordx(Point p) { return 400 + zoom * (p.real() - centerX); }
int cordy(Point p) { return 400 - zoom * (p.imag() - centerY); }

#define cord(p) cordx(p), cordy(p)

void draw_point(Point p) {
  fprintf(stderr, "circle(%d, %d, %d)\n", cord(p), 2);
}

void draw_segment(Line l) {
  fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(l.a), cord(l.b));
}

void draw_line(Line l) {
  Point v = l.b - l.a;
  Line m(l.a - v * Point(1e4, 0), l.b + v * Point(1e4, 0));
  fprintf(stderr, "line(%d, %d, %d, %d)\n", cord(m.a), cord(m.b));
}

void draw_polygon(const Polygon &p) {
  int n = p.size();
  REP(i, n) draw_segment(Line(p[i], p[(i + 1) % n]));
}

void draw_circle(Circle c) {
  fprintf(stderr, "circle(%d, %d, %d)\n", cord(c.p), (int)(zoom * c.r));
}

int main() {
  int n;
  while (cin >> n, n) {
    vector<Circle> Curls(n);
    for (int i = 0; i < n; ++i) {
      int x, y;
      cin >> x >> y;
      Point p(x, y);
      int r;
      cin >> r;
      Curls[i] = Circle(p, r);
    }
    vector<Line> ls;
    ls.push_back(Line(Curls[0].p, Curls[0].p));
    for (int i = 0; i < n - 1; ++i) {
      auto l = is_cc(Curls[i], Curls[i + 1]);
      ls.push_back(Line(l[0], l[1]));
    }
    ls.push_back(Line(Curls[n - 1].p, Curls[n - 1].p));
    vector<vector<ld>> dist(2 * n + 2, vector<ld>(2 * n + 2, 1e9));
    for (int i = 0; i < (n + 1) * 2; ++i) {
      for (int j = i + 1; j < (n + 1) * 2; ++j) {
        Line s;
        if (i % 2 == 0 && j % 2 == 0)
          s = Line(ls[i / 2].a, ls[j / 2].a);
        else if (i % 2 && j % 2)
          s = Line(ls[i / 2].b, ls[j / 2].b);
        else if (i % 2 == 0 && j % 2)
          s = Line(ls[i / 2].a, ls[j / 2].b);
        else if (i % 2 && j % 2 == 0)
          s = Line(ls[i / 2].b, ls[j / 2].a);
        bool flag = 1;
        for (int k = i / 2 + 1; k < j / 2; ++k) {
          if (isis_ss(s, ls[k]) == 0) {
            flag = 0;
            break;
          }
        }
        Point c = s.a - s.b;
        if (flag) dist[i][j] = sqrtl(c.imag() * c.imag() + c.real() * c.real());
      }
    }
    for (int k = 0; k < 2 * n + 2; ++k) {
      for (int i = 0; i < 2 * n + 2; ++i) {
        for (int j = 0; j < 2 * n + 2; ++j) {
          if (dist[i][j] > dist[i][k] + dist[k][j]) {
            dist[i][j] = dist[i][k] + dist[k][j];
          }
        }
      }
    }
    cout << fixed << setprecision(6) << dist[0][2 * n + 1] << endl;
  }
}


Measured memory_bytes: 28476