#include <iostream>
#include <cstdio>
#include <vector>
#include <algorithm>
#include <complex>
#include <cstring>
#include <cstdlib>
#include <string>
#include <cmath>
#include <cassert>
#include <queue>
#include <set>
#include <map>
#include <valarray>
#include <bitset>
#include <stack>
using namespace std;

#define REP(i,n) for(int i=0;i<(int)n;++i)
#define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();++i)
#define ALL(c) (c).begin(), (c).end()
typedef long long ll;
const int INF = 1<<29;
const double PI = acos(-1);
const double EPS = 1e-8;

typedef complex<double> P;
namespace std {
  bool operator < (const P& a, const P& b) {
    return real(a) != real(b) ? real(a) < real(b) : imag(a) < imag(b);
  }
}
double cross(const P& a, const P& b) {
  return imag(conj(a)*b);
}
double dot(const P& a, const P& b) {
  return real(conj(a)*b);
}
struct L : public vector<P> {
  L(const P &a, const P &b) {
    push_back(a); push_back(b);
  }
};
typedef vector<P> G;
#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
struct C {
  P p; double r;
  C(const P &p, double r) : p(p), r(r) { }
};

int ccw(P a, P b, P c) {
  b -= a; c -= a;
  if (cross(b, c) > 0)   return +1;       // counter clockwise
  if (cross(b, c) < 0)   return -1;       // clockwise
  if (dot(b, c) < 0)     return +2;       // c--a--b on line
  if (norm(b) < norm(c)) return -2;       // a--b--c on line
  return 0;
}

bool intersectLS(const L &l, const L &s) {
  return cross(l[1]-l[0], s[0]-l[0])*       // s[0] is left of l
         cross(l[1]-l[0], s[1]-l[0]) < EPS; // s[1] is right of l
}

bool intersectLL(const L &l, const L &m) {
  return abs(cross(l[1]-l[0], m[1]-m[0])) > EPS || // non-parallel
         abs(cross(l[1]-l[0], m[0]-l[0])) < EPS;   // same line
}
P crosspoint(const L &l, const L &m) {
  double A = cross(l[1] - l[0], m[1] - m[0]);
  double B = cross(l[1] - l[0], l[1] - m[0]);
  if (abs(A) < EPS && abs(B) < EPS) return m[1]; // same line
  if (abs(A) < EPS) assert(false); // !!!PRECONDITION NOT SATISFIED!!!
  return m[0] + B / A * (m[1] - m[0]);
}

struct S {
  int l, r;
  double d;
  S(int l, int r, double d) : l(l),r(r),d(d) {}
};

const bool operator<(const S &a, const S &b) {
  return a.d > b.d;
}

int main() {
  int n;
  while(cin >> n, n) {
    //cout << n << endl;
    P p[n];
    set<int> hset;
    vector<P> v;
    REP(i, n) {
      int x, y;
      cin >> x >> y;
      p[i] = P(x,y);
      hset.insert(y);
      v.push_back(p[i]);
    }
    FOR(it, hset) {
      REP(i, n-1) {
        L l1(P(0,*it),P(1,*it)), l2(p[i+1],p[i]);
        if (intersectLS(l1, l2)) {
          P a = crosspoint(l1, l2);
          v.push_back(a);
        }
      }
    }
    
    sort(ALL(v));
    v.erase(unique(ALL(v)), v.end());
    // FOR(it, v) cout << *it;
    // cout << endl;
    int m = v.size();
    // vector<double> dis(m-1);;
    // REP(i, m-1) {
    //   dis[i] = abs(v[i] - v[i+1]);
    //   //cout << dis[i] << " ";
    // }
    //cout << endl;
    vector<int> height(m);
    REP(i, m) {
      height[i] = v[i].imag() + 0.5;
      //printf("%d ",height[i]);
    }
    //cout << endl;
    typedef pair<int,int> pii;
    priority_queue<S> Q;
    Q.push(S(0, m-1, 0));
    map<pii, double> dist;
    dist[pii(0,m-1)] = 0;
    //cout << m << endl;
    int d[3] = {-1,0,1};
    double ans = -1;
    while(!Q.empty()) {
      S p = Q.top(); Q.pop();
      int left = p.l, right = p.r;
      // printf("%d(%d), %d(%d)\n", left,height[left],right,height[right]);
      // cout << left << " " << right << endl;
      if (left == right) {
        ans = dist[pii(left,right)];
        break;
      }
      if (dist[pii(left,right)] < p.d) continue;
      REP(i, 3) {
        REP(j, 3) {
          int l = left+d[i];
          int r = right+d[j];
          if (l<0||l>=m||r<0||r>=m) continue;
          if (l <= r && height[l] == height[r]) {
            double len = abs(v[left]-v[l]) + abs(v[right]-v[r]);
            double dis = dist[pii(left,right)] + len;
            if (dist.count(pii(l,r)) == 0 || dist[pii(l,r)] > dis) {
              dist[pii(l,r)] = dis;
              Q.push(S(l,r,dis));
            }
          }
        }
      } 
    }
    printf("%.3f\n", ans);
  }
}

Measured memory_bytes: 0