Problem: There is a chain consisting of multiple circles on a plane. The first (last) circle of the chain only intersects with the next (previous) circle, and each intermediate circle intersects only with the two neighboring circles.

Your task is to find the shortest path that satisfies the following conditions.

* The path connects the centers of the first circle and the last circle.
* The path is confined in the chain, that is, all the points on the path are located within or on at least one of the circles.

Figure E-1 shows an example of such a chain and the corresponding shortest path.

<image>

Figure E-1: An example chain and the corresponding shortest path


Input

The input consists of multiple datasets. Each dataset represents the shape of a chain in the following format.

> n
>  x1 y1 r1
>  x2 y2 r2
>  ...
>  xn yn rn
>

The first line of a dataset contains an integer n (3 ≤ n ≤ 100) representing the number of the circles. Each of the following n lines contains three integers separated by a single space. (xi, yi) and ri represent the center position and the radius of the i-th circle Ci. You can assume that 0 ≤ xi ≤ 1000, 0 ≤ yi ≤ 1000, and 1 ≤ ri ≤ 25.

You can assume that Ci and Ci+1 (1 ≤ i ≤ n−1) intersect at two separate points. When j ≥ i+2, Ci and Cj are apart and either of them does not contain the other. In addition, you can assume that any circle does not contain the center of any other circle.

The end of the input is indicated by a line containing a zero.

Figure E-1 corresponds to the first dataset of Sample Input below. Figure E-2 shows the shortest paths for the subsequent datasets of Sample Input.

<image>

Figure E-2: Example chains and the corresponding shortest paths


Output

For each dataset, output a single line containing the length of the shortest chain-confined path between the centers of the first circle and the last circle. The value should not have an error greater than 0.001. No extra characters should appear in the output.

Sample Input


10
802 0 10
814 0 4
820 1 4
826 1 4
832 3 5
838 5 5
845 7 3
849 10 3
853 14 4
857 18 3
3
0 0 5
8 0 5
8 8 5
3
0 0 5
7 3 6
16 0 5
9
0 3 5
8 0 8
19 2 8
23 14 6
23 21 6
23 28 6
19 40 8
8 42 8
0 39 5
11
0 0 5
8 0 5
18 8 10
8 16 5
0 16 5
0 24 5
3 32 5
10 32 5
17 28 8
27 25 3
30 18 5
0


Output for the Sample Input


58.953437
11.414214
16.0
61.874812
63.195179






Example

Input

10
802 0 10
814 0 4
820 1 4
826 1 4
832 3 5
838 5 5
845 7 3
849 10 3
853 14 4
857 18 3
3
0 0 5
8 0 5
8 8 5
3
0 0 5
7 3 6
16 0 5
9
0 3 5
8 0 8
19 2 8
23 14 6
23 21 6
23 28 6
19 40 8
8 42 8
0 39 5
11
0 0 5
8 0 5
18 8 10
8 16 5
0 16 5
0 24 5
3 32 5
10 32 5
17 28 8
27 25 3
30 18 5
0


Output

58.953437
11.414214
16.0
61.874812
63.195179

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
template<typename T>
struct Edge {
    int from, to;
    T cost;
    Edge(int from, int to, T cost) {
        this->from = from;
        this->to = to;
        this->cost = cost;
    }
};
bool operator == (Edge<int> e1, Edge<int> e2) {
    return e1.from == e2.from &&
            e1.to == e2.to &&
            e1.cost == e2.cost;
}
bool operator > (Edge<int> e1, Edge<int> e2) {
    return e1.cost < e2.cost;
}
template<typename T>
using Edges = std::vector<Edge<T>>;
template<typename T>
using Graph = std::vector<Edges<T>>;
template <typename T>
std::vector<T> dijkstra(const Graph<T> &g, int s) {
    int sz = (int)(g.size());
    std::vector<T> dist(sz, -1);
    std::priority_queue<std::pair<T, int>, std::vector<std::pair<T, int>>, std::greater<std::pair<T, int>>> pq;
    dist[s] = 0;
    pq.push({0, s});
    while(!pq.empty()) {
        T d = pq.top().first;
        int now = pq.top().second;
        pq.pop();
        if(dist[now] == -1 || d > dist[now]) continue;
        for(int i=0;i<(int)(g[now].size());++i) {
            int next = g[now][i].to;
            T cost = g[now][i].cost;
            if(dist[next] == -1 || dist[next] > dist[now] + cost) {
                dist[next] = dist[now] + cost;
                pq.push({cost, next});
            }
        }
    }
    return dist;
}
using namespace std;
using ll = long long;
using ld = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vector<int>>;
using vll = vector<ll>;
using vvll = vector<vector<ll>>;
const double eps = 1e-10;
const ll MOD = 1000000007;
const int INF = 1000000000;
const ll LINF = 1ll<<50;
template<typename T>
void printv(const vector<T>& s) {
  for(int i=0;i<(int)(s.size());++i) {
    cout << s[i];
    if(i == (int)(s.size())-1) cout << endl;
    else cout << " ";
  }
}
template<typename T1, typename T2>
ostream& operator<<(ostream &os, const pair<T1, T2> p) {
  os << p.first << ":" << p.second;
  return os;
}
using Point = std::complex<ld>;
const ld 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();
}
}
Point input_point() {
  ld x, y;
  std::cin >> x >> y;
  return Point(x, y);
}
bool eq(ld a, ld b) { return (abs(a - b) < eps); }
ld dot(Point a, Point b) { return real(conj(a) * b); }
ld cross(Point a, Point b) { return imag(conj(a) * b); }
int ccw(Point a, Point b, Point c) {
  b -= a;
  c -= a;
  if (cross(b, c) > eps) return 1;
  if (cross(b, c) < -eps) return -1;
  if (dot(b, c) < 0) return 2;
  if (norm(b) < norm(c)) return -2;
  return 0;
}
class Line {
 public:
  Point a, b;
  Line() : a(Point(0, 0)), b(Point(0, 0)) {}
  Line(Point a, Point b) : a(a), b(b) {}
};
ld dot(Line l, Line m) { return dot((l.a - l.b), (m.a - m.b)); }
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 l, Line m) {
  Point lv = l.b - l.a, mv = m.b - m.a;
  assert(cross(lv, mv) != 0);
  return l.a + lv * cross(mv, m.a - l.a) / cross(mv, lv);
}
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 : std::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) : std::min(abs(s.a - p), abs(s.b - p));
}
ld dist_ss(Line s, Line t) {
  if (isis_ss(s, t)) return 0;
  return std::min(
      {dist_sp(s, t.a), dist_sp(s, t.b), dist_sp(t, s.a), dist_sp(t, s.b)});
}
Line bisector(Point a, Point b) {
  Point mid = (a + b) * Point(0.5, 0);
  return Line(mid, mid + (b - a) * Point(0, pi / 2));
}
ld degree_ll(Line l, Line m) {
  ld cos_shita = dot(l, m) / (abs(l.b - l.a) * abs(m.b - m.a));
  if (cos_shita < -1.0) cos_shita = -1.0;
  if (cos_shita > 1.0) cos_shita = 1.0;
  ld shita = acos(cos_shita);
  return shita;
}
class Circle {
 public:
  Point p;
  ld r;
  Circle() : p(Point(0, 0)), r(0) {}
  Circle(Point p, ld r) : p(p), r(r) {}
};
std::vector<Point> is_cc(Circle c1, Circle c2) {
  std::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.emplace_back(c1.p + diff * Point(rc, rs));
  if (dfr != 0.0) res.emplace_back(c1.p + diff * Point(rc, -rs));
  return res;
}
std::vector<Point> is_lc(Circle c, Line l) {
  std::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.emplace_back(proj(l, c.p) + len * nor);
    res.emplace_back(proj(l, c.p) - len * nor);
  }
  return res;
}
std::vector<Point> is_sc(Circle c, Line l) {
  std::vector<Point> v = is_lc(c, l), res;
  for (Point p : v)
    if (isis_sp(l, p)) res.emplace_back(p);
  return res;
}
std::vector<Line> tangent_cp(Circle c, Point p) {
  std::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.emplace_back(Line(p, p + v1));
  if (l < eps) return ret;
  ret.emplace_back(Line(p, p + v2));
  return ret;
}
void solve(int n) {
  vector<Circle> circles;
  for(int i=0;i<n;++i) {
    Point p = input_point();
    ld r; cin >> r;
    circles.emplace_back(Circle(p, r));
  }
  Point s = circles[0].p, g = circles[n-1].p;
  vector<Point> p0(n-1), p1(n-1);
  for(int i=0;i<n-1;++i) {
    auto res = is_cc(circles[i], circles[i+1]);
    p0[i] = res[0];
    p1[i] = res[1];
  }
  Graph<ld> graph(2*n);
  Line line(s, g);
  bool ok = true;
  for(int i=0;i<n-1;++i) {
    ld lp0 = cross(line.b - line.a, p0[i] - line.a), lp1 = cross(line.b - line.a, p1[i] - line.a);
    ok &= (signbit(lp0) != signbit(lp1));
  }
  if(ok) graph[0].push_back(Edge<ld>(0, 2*n-1, abs(s - g)));
  for(int i=0;i<n-1;++i) {
    Line l0(s, p0[i]), l1(s, p1[i]);
    bool ok0 = true, ok1 = true;
    for(int j=0;j<i;++j) {
      ld l0p0 = cross(l0.b - l0.a, p0[j] - l0.a), l0p1 = cross(l0.b - l0.a, p1[j] - l0.a);
      ld l1p0 = cross(l1.b - l1.a, p0[j] - l1.a), l1p1 = cross(l1.b - l1.a, p1[j] - l1.a);
      ok0 &= (signbit(l0p0) != signbit(l0p1));
      ok1 &= (signbit(l1p0) != signbit(l1p1));
    }
    if(ok0) graph[0].push_back(Edge<ld>(0, 1 + i*2, abs(s - p0[i])));
    if(ok1) graph[0].push_back(Edge<ld>(0, 2 + i*2, abs(s - p1[i])));
  }
  for(int i=0;i<n-1;++i) {
    Line l0(p0[i], g), l1(p1[i], g);
    bool ok0 = true, ok1 = true;
    for(int j=i+1;j<n-1;++j) {
      ld l0p0 = cross(l0.b - l0.a, p0[j] - l0.a), l0p1 = cross(l0.b - l0.a, p1[j] - l0.a);
      ld l1p0 = cross(l1.b - l1.a, p0[j] - l1.a), l1p1 = cross(l1.b - l1.a, p1[j] - l1.a);
      ok0 &= (signbit(l0p0) != signbit(l0p1));
      ok1 &= (signbit(l1p0) != signbit(l1p1));
    }
    if(ok0) graph[1+i*2].push_back(Edge<ld>(1+i*2, 2*n-1, abs(g - p0[i])));
    if(ok1) graph[2+i*2].push_back(Edge<ld>(2+i*2, 2*n-1, abs(g - p1[i])));
  }
  for(int i=0;i<n-2;++i) {
    for(int j=i+1;j<n-1;++j) {
      Line l0(p0[i], p0[j]), l1(p0[i], p1[j]), l2(p1[i], p0[j]), l3(p1[i], p1[j]);
      bool ok0 = true, ok1 = true, ok2 = true, ok3 = true;
      for(int k=i+1;k<j;++k) {
        ld l0p0 = cross(l0.b - l0.a, p0[k] - l0.a), l0p1 = cross(l0.b - l0.a, p1[k] - l0.a);
        ld l1p0 = cross(l1.b - l1.a, p0[k] - l1.a), l1p1 = cross(l1.b - l1.a, p1[k] - l1.a);
        ld l2p0 = cross(l2.b - l2.a, p0[k] - l2.a), l2p1 = cross(l2.b - l2.a, p1[k] - l2.a);
        ld l3p0 = cross(l3.b - l3.a, p0[k] - l3.a), l3p1 = cross(l3.b - l3.a, p1[k] - l3.a);
        ok0 &= (signbit(l0p0) != signbit(l0p1));
        ok1 &= (signbit(l1p0) != signbit(l1p1));
        ok2 &= (signbit(l2p0) != signbit(l2p1));
        ok3 &= (signbit(l3p0) != signbit(l3p1));
      }
      if(ok0) graph[1+i*2].push_back(Edge<ld>(1+i*2, 1+j*2, abs(p0[i] - p0[j])));
      if(ok1) graph[1+i*2].push_back(Edge<ld>(1+i*2, 2+j*2, abs(p0[i] - p1[j])));
      if(ok2) graph[2+i*2].push_back(Edge<ld>(2+i*2, 1+j*2, abs(p1[i] - p0[j])));
      if(ok3) graph[2+i*2].push_back(Edge<ld>(2+i*2, 2+j*2, abs(p1[i] - p1[j])));
    }
  }
  cout << dijkstra(graph, 0)[2*n-1] << endl;
}
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(10);
  while(1) {
    int n; cin >> n;
    if(n == 0) break;
    solve(n);
  }
}