#include <bits/stdc++.h>

using namespace std;

//typedef
//------------------------------------------
typedef vector<int> VI;
typedef vector<VI> VVI;
typedef vector<string> VS;
typedef pair<double, int> PDI;
typedef long long LL;

//container util
//------------------------------------------
#define ALL(a)  (a).begin(),(a).end()
#define RALL(a) (a).rbegin(), (a).rend()
#define PB push_back
#define MP make_pair
#define SZ(a) int((a).size())
#define EACH(i,c) for(typeof((c).begin()) i=(c).begin(); i!=(c).end(); ++i)
#define EXIST(s,e) ((s).find(e)!=(s).end())
#define SORT(c) sort((c).begin(),(c).end())

//repetition
//------------------------------------------
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)

//constant
//--------------------------------------------
const double EPS = 1e-10;
const double PI  = acos(-1.0);
const double INF = 1e9;
struct Edge{
  int to;
  double cost;

  Edge(int t, double c): to(t), cost(c)
  {}
  bool operator>(const Edge& rhs) const{
	return cost > rhs.cost;
  }
};
typedef vector< vector<Edge> > Graph;

int N;

double dist(PDI p1, PDI p2){
  return sqrt((p1.first-p2.first)*(p1.first-p2.first)
			  +(p1.second-p2.second)*(p1.second-p2.second));
}


void Dijkstra(const Graph& edges, vector<double>& d, int s){
  priority_queue<PDI, vector<PDI>, greater<PDI> > pq;
  fill(d.begin(), d.end(), INF);
  d[s] = 0;
  pq.push(MP(0,s));

  while(!pq.empty()){
	PDI pii = pq.top(); pq.pop();
	int v = pii.second;
	if(d[v] < pii.first) continue;
	for(unsigned int i=0;i<edges[v].size();++i){
	  const Edge& e = edges[v][i];
	  if(d[e.to] > d[v] + e.cost){
		d[e.to] = d[v] + e.cost;
		pq.push(MP(d[e.to], e.to));
	  }
	}
  }
}


int main(){
  cin.tie(0);
  ios_base::sync_with_stdio(false);

  while(cin>>N,N){
	set<int> ys;
	vector<PDI> xy;
	REP(i,N){
	  int x, y; cin >> x >> y;
	  xy.emplace_back(x,y);
	  ys.insert(y);
	}
	for(int i=0;i+1<SZ(xy);++i){
	  if(xy[i].second < xy[i+1].second){
		auto it = ys.upper_bound(xy[i].second);
		if(it != ys.end() && *it < xy[i+1].second){
		  xy.insert(xy.begin()+i+1,
					MP(xy[i].first+(*it-xy[i].second)*(xy[i+1].first-xy[i].first)*1.
					   /(xy[i+1].second-xy[i].second),*it));
		}
	  }
	  else{
		auto it = ys.lower_bound(xy[i].second);
		if(it == ys.begin()) continue;
		--it;
		if(*it > xy[i+1].second){
		  xy.insert(xy.begin()+i+1,
					MP(xy[i].first+(*it-xy[i].second)*(xy[i+1].first-xy[i].first)*1.
					   /(xy[i+1].second-xy[i].second),*it));
		}
	  }
	}
	N = SZ(xy);
	/*
	Graph G(N*N, vector<Edge>());
	for(int i=0;i<N*N;++i){
	  int a = i / N, b = i % N;
	  for(int da=-1;da<=1;++da)
		for(int db=-1;db<=1;++db){
		  if(da == 0 && db == 0) continue;
		  int a_ = a + da, b_ = b + db;
		  if(!(0 <= a_ && a_ < N && 0 <= b_ && b_ < N && a_ <= b_)) continue;
		  if(xy[a_].second != xy[b_].second) continue;
		  int j = a_ * N + b_;
		  G[i].emplace_back(j, dist(xy[a],xy[a_])+dist(xy[b],xy[b_]));
		}
	}
	*/
	map<int,double> d;
	priority_queue<PDI, vector<PDI>, greater<PDI> > pq;
	d[N-1] = 0;
	pq.push(MP(0,N-1));

	while(!pq.empty()){
	  PDI pii = pq.top(); pq.pop();
	  int v = pii.second;
	  if(d[v] < pii.first) continue;
	  int a = v / N, b = v % N;
	  for(int da=-1;da<=1;++da)
		for(int db=-1;db<=1;++db){
		  if(da == 0 && db == 0) continue;
		  int a_ = a + da, b_ = b + db;
		  if(!(0 <= a_ && a_ < N && 0 <= b_ && b_ < N && a_ <= b_)) continue;
		  if(xy[a_].second != xy[b_].second) continue;
		  int j = a_ * N + b_;
		  double cost = dist(xy[a],xy[a_])+dist(xy[b],xy[b_]);
		  if(!d.count(j) || d[j] > d[v] + cost){
			d[j] = d[v] + cost;
			pq.push(MP(d[j], j));
		  }
		}
	}

	double ans = INF;
	REP(i,N) ans = min(ans, d[i*N+i]);
	
	cout << fixed << setprecision(9) << ans << endl;
  }

  return 0;
}

Measured memory_bytes: 4304