#define  _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES

#pragma comment (linker, "/STACK:526000000")

#include "bits/stdc++.h"

using namespace std;
typedef string::const_iterator State;
#define eps 1e-10L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define seg_size 262144LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))
#define ALL(x) (x).begin(),(x).end()

typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;

typedef struct Circle {
    complex<long double> center;
    long double r;
}Circle;

long double dot(Point a, Point b) {
    return (a.real() * b.real() + a.imag() * b.imag());
}
long double cross(Point a, Point b) {
    return (a.real() * b.imag() - a.imag() * b.real());
}

long double Dist_Line_Point(Line a, Point b) {
    if (dot(a.second - a.first, b - a.first) < eps) return abs(b - a.first);
    if (dot(a.first - a.second, b - a.second) < eps) return abs(b - a.second);
    return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}

int is_intersected_ls(Line a, Line b) {
    return (cross(a.second - a.first, b.first - a.first) * cross(a.second - a.first, b.second - a.first) < 0) &&
        (cross(b.second - b.first, a.first - b.first) * cross(b.second - b.first, a.second - b.first) < 0);
}

Point intersection_l(Line a, Line b) {
    Point da = a.second - a.first;
    Point db = b.second - b.first;
    return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}

long double Dist_Line_Line(Line a, Line b) {
    if (is_intersected_ls(a, b) == 1) {
        return 0;
    }
    return min({ Dist_Line_Point(a,b.first), Dist_Line_Point(a,b.second),Dist_Line_Point(b,a.first),Dist_Line_Point(b,a.second) });
}

pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
    long double dist = abs(a.center - b.center);
    assert(dist <= eps + a.r + b.r);
    assert(dist+eps >= abs(a.r - b.r));
    Point target = b.center - a.center;
    long double pointer = target.real() * target.real() + target.imag() * target.imag();
    long double aa = pointer + a.r * a.r - b.r * b.r;
    aa /= 2.0L;
    Point l{ (aa * target.real() + target.imag() * sqrt(pointer * a.r * a.r - aa * aa))/pointer,
            (aa* target.imag() - target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer};
    Point r{ (aa * target.real() - target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
        (aa * target.imag() + target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
    r = r + a.center;
    l = l + a.center;
    return mp(l, r);
}
void init() {
    iostream::sync_with_stdio(false);
    cout << fixed << setprecision(20);
}

unsigned long xor128() {
    static unsigned long x = 123456789, y = 362436069, z = 521288629, w = 88675123;
    unsigned long t = (x ^ (x << 11));
    x = y; y = z; z = w;
    return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}

#define int ll
void solve(){
    vector<long double> answ;
    while (true) {
        int n;
        cin >> n;
        if (n == 0) {
            REP(i, answ.size()) {
                cout << answ[i] << endl;
            }
            return;
        }
        vector<Circle> inputs;
        REP(i, n) {
            long double a, b, c;
            cin >> a >> b >> c;
            inputs.push_back(Circle{ Point{a,b},c });
        }
        vector<Line> barriers;
        REP(i, n - 1) {
            barriers.push_back(intersection_Circle_Circle(inputs[i], inputs[i + 1]));
        }
        long double dp[101][2] = {};
        REP(i, n-1) {
            dp[i][0] = 1e9;
            dp[i][1] = 1e9;
            for (int j = 0; j < i; ++j) {
                {
                    int ok = 1;
                    for (int t = j+1; t < i; ++t) {
                        if (is_intersected_ls(barriers[t], Line{ barriers[j].first,barriers[i].first }) == 0) {
                            ok = 0;
                            break;
                        }
                    }
                    if (ok == 1) {
                        dp[i][0] = min(dp[i][0], dp[j][0] + abs(barriers[i].first - barriers[j].first));
                    }
                }
                {
                    int ok = 1;
                    for (int t = j + 1; t < i; ++t) {
                        if (is_intersected_ls(barriers[t], Line{ barriers[j].second,barriers[i].first }) == 0) {
                            ok = 0;
                            break;
                        }
                    }
                    if (ok == 1) {
                        dp[i][0] = min(dp[i][0], dp[j][1] + abs(barriers[i].first - barriers[j].second));
                    }
                }
                {
                    int ok = 1;
                    for (int t = j + 1; t < i; ++t) {
                        if (is_intersected_ls(barriers[t], Line{ barriers[j].second,barriers[i].second }) == 0) {
                            ok = 0;
                            break;
                        }
                    }
                    if (ok == 1) {
                        dp[i][1] = min(dp[i][1], dp[j][1] + abs(barriers[i].second - barriers[j].second));
                    }
                }
                {
                    int ok = 1;
                    for (int t = j + 1; t < i; ++t) {
                        if (is_intersected_ls(barriers[t], Line{ barriers[j].first,barriers[i].second }) == 0) {
                            ok = 0;
                            break;
                        }
                    }
                    if (ok == 1) {
                        dp[i][1] = min(dp[i][1], dp[j][0] + abs(barriers[i].second - barriers[j].first));
                    }
                }
            }
            
            {
                int ok = 1;
                REP(j,i){
                    if (is_intersected_ls(barriers[j], Line{ inputs[0].center,barriers[i].first }) == 0) {
                        ok = 0;
                        break;
                    }
                }
                if (ok == 1) {
                    dp[i][0] = min(dp[i][0], abs(barriers[i].first - inputs[0].center));
                }
            }
            {
                int ok = 1;
                REP(j, i) {
                    if (is_intersected_ls(barriers[j], Line{ inputs[0].center,barriers[i].second }) == 0) {
                        ok = 0;
                        break;
                    }
                }
                if (ok == 1) {
                    dp[i][1] = min(dp[i][1], abs(barriers[i].second - inputs[0].center));
                }
            }
        }
        long double ans = 1e9;
        for (int j = n - 2; j >= 0; --j) {
            {
                int ok = 1;
                for (int t = j + 1; t < n - 1;++t) {
                    if (is_intersected_ls(barriers[t], Line{ inputs.back().center,barriers[j].first }) == 0) {
                        ok = 0;
                        break;
                    }
                }
                if (ok == 1) {
                    ans = min(ans, dp[j][0] + abs(barriers[j].first - inputs.back().center));
                }
            }
            {
                int ok = 1;
                for (int t = j + 1; t < n - 1; ++t) {
                    if (is_intersected_ls(barriers[t], Line{ inputs.back().center,barriers[j].second }) == 0) {
                        ok = 0;
                        break;
                    }
                }
                if (ok == 1) {
                    ans = min(ans, dp[j][1] + abs(barriers[j].second - inputs.back().center));
                }
            }
        }
        {
            int ok = 1;
            for (int t = 0; t < barriers.size(); ++t) {
                if (is_intersected_ls(barriers[t], Line{ inputs.back().center,inputs[0].center }) == 0) {
                    ok = 0;
                    break;
                }
            }
            if (ok == 1) {
                ans = min(ans, abs(inputs[0].center - inputs.back().center));
            }
        }
        answ.push_back(ans);
        //cout << ans << endl;
    }
}

#undef int
int main() {
    init();
    solve();
}


Measured memory_bytes: 3352