#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const double eps = 1e-12;
const int step[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <class T>
inline T max1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a > b ? a : b;
  if (c != -1234567) ans = max1(ans, c);
  if (d != -1234567) ans = max1(ans, d);
  return ans;
}
template <class T>
inline T min1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a < b ? a : b;
  if (c != -1234567) ans = min(ans, c);
  if (d != -1234567) ans = min(ans, d);
  return ans;
}
template <class T>
inline T gcd1(T a, T b) {
  if (a < b) swap(a, b);
  if (a % b == 0) return b;
  return gcd1(b, a % b);
}
template <class T>
inline T lb(T num) {
  return num & (-num);
}
inline int jud(double a, double b) {
  if (abs1(a - b) < eps) return 0;
  if (a < b) return -1;
  return 1;
}
template <class t>
inline int find(t val, t* a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 1) return 0;
  int be = 0, en = na - 1;
  if (a[0] <= a[na - 1]) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(a[mid], val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(a[mid], val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(a[be], val) == 1 && be != 0) be--;
    if (!f_small && jud(a[be], val) == -1 && be != na - 1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(a[mid], val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(a[mid], val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(a[be], val) == -1 && be != 0) be--;
    if (f_small && jud(a[be], val) == 1 && be != na - 1) be++;
  }
  return be;
}
inline int bitnum(unsigned long long nValue) {
  nValue = ((0xaaaaaaaaaaaaaaaaull & nValue) >> 1) +
           (0x5555555555555555ull & nValue);
  nValue = ((0xccccccccccccccccull & nValue) >> 2) +
           (0x3333333333333333ull & nValue);
  nValue = ((0xf0f0f0f0f0f0f0f0ull & nValue) >> 4) +
           (0x0f0f0f0f0f0f0f0full & nValue);
  nValue = ((0xff00ff00ff00ff00ull & nValue) >> 8) +
           (0x00ff00ff00ff00ffull & nValue);
  nValue = ((0xffff0000ffff0000ull & nValue) >> 16) +
           (0x0000ffff0000ffffull & nValue);
  nValue = ((0xffffffff00000000ull & nValue) >> 32) +
           (0x00000000ffffffffull & nValue);
  return nValue;
}
long long pow(long long n, long long m, long long mod = 0) {
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
template <int MAXN, typename T = int, typename S = T>
struct MinCostMaxFlow {
  struct NegativeCostCircuitExistsException {};
  struct Edge {
    int v;
    T c;
    S w;
    int b;
    Edge(int v, T c, S w, int b) : v(v), c(c), w(w), b(b) {}
  };
  int n, source, sink;
  vector<Edge> e[MAXN];
  void init(int n, int source, int sink) {
    this->n = n;
    this->source = source;
    this->sink = sink;
    for (int i = 0; i < n; ++i) {
      e[i].clear();
    }
  }
  void addEdge(int a, int b, T c, S w) {
    e[a].push_back(Edge(b, c, w, e[b].size()));
    e[b].push_back(Edge(a, 0, -w, e[a].size() - 1));
  }
  bool mark[MAXN];
  T maxc[MAXN];
  S minw[MAXN];
  int dist[MAXN];
  Edge* prev[MAXN];
  bool _spfa() {
    queue<int> q;
    fill(mark, mark + n, false);
    fill(maxc, maxc + n, 0);
    fill(minw, minw + n, numeric_limits<S>::max());
    fill(dist, dist + n, 0);
    fill(prev, prev + n, (Edge*)NULL);
    mark[source] = true;
    maxc[source] = numeric_limits<T>::max();
    minw[source] = 0;
    q.push(source);
    while (!q.empty()) {
      int cur = q.front();
      mark[cur] = false;
      q.pop();
      for (typename vector<Edge>::iterator it = e[cur].begin();
           it != e[cur].end(); ++it) {
        T c = min(maxc[cur], it->c);
        if (c == 0) {
          continue;
        }
        int v = it->v;
        S w = minw[cur] + it->w;
        if (minw[v] > w + eps || (fabs(minw[v] - w) < eps && maxc[v] < c)) {
          maxc[v] = c;
          minw[v] = w;
          dist[v] = dist[cur] + 1;
          if (dist[v] >= n) {
            return false;
          }
          prev[v] = &*it;
          if (!mark[v]) {
            mark[v] = true;
            q.push(v);
          }
        }
      }
    }
    return true;
  }
  pair<T, S> gao() {
    T sumc = 0;
    S sumw = 0;
    while (true) {
      if (!_spfa()) {
        throw NegativeCostCircuitExistsException();
      } else if (maxc[sink] == 0) {
        break;
      } else {
        T c = maxc[sink];
        sumc += c;
        sumw += c * minw[sink];
        int cur = sink;
        while (cur != source) {
          Edge* e1 = prev[cur];
          e1->c -= c;
          Edge* e2 = &e[e1->v][e1->b];
          e2->c += c;
          cur = e2->v;
        }
      }
    }
    return make_pair(sumc, sumw);
  }
};
const int MAXN = 1010;
MinCostMaxFlow<MAXN, int, double> g;
const int maxn = 500;
struct node {
  int x, y;
  bool operator<(const node& a) const { return y > a.y; }
} orig[maxn];
int n;
long double dis(int x1, int y1, int x2, int y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
int main() {
  scanf("%d", &n);
  for (int j = 0; j < n; j++) scanf("%d%d", &orig[j].x, &orig[j].y);
  sort(orig, orig + n);
  if (orig[0].y <= orig[1].y) {
    cout << -1 << endl;
    return 0;
  }
  g.init(n * 2 + 2, 0, 2 * n + 1);
  for (int i = 1; i < n; i++) g.addEdge(0, i + 1, 1, 0);
  for (int i = 1; i < n; i++)
    for (int j = 0; j < i; j++)
      if (orig[j].y > orig[i].y)
        g.addEdge(i + 1, j + n + 1, 1,
                  dis(orig[i].x, orig[i].y, orig[j].x, orig[j].y));
  for (int i = 0; i < n; i++) g.addEdge(i + n + 1, n * 2 + 1, 2, 0);
  pair<int, double> ans = g.gao();
  if (ans.first != n - 1) {
    cout << -1 << endl;
    return 0;
  }
  cout << fixed << setprecision(15) << ans.second << endl;
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

A root tree is a directed acyclic graph that contains one node (root), from which there is exactly one path to any other node.

A root tree is binary if each node has at most two outgoing arcs.

When a binary tree is painted on the plane, all arcs should be directed from top to bottom. That is, each arc going from u to v must meet the condition yu > yv.

You've been given the coordinates of all tree nodes. Your task is to connect these nodes by arcs so as to get the binary root tree and make the total length of the arcs minimum. All arcs of the built tree must be directed from top to bottom.

Input

The first line contains a single integer n (2 ≤ n ≤ 400) — the number of nodes in the tree. Then follow n lines, two integers per line: xi, yi (|xi|, |yi| ≤ 103) — coordinates of the nodes. It is guaranteed that all points are distinct.

Output

If it is impossible to build a binary root tree on the given points, print "-1". Otherwise, print a single real number — the total length of the arcs in the minimum binary tree. The answer will be considered correct if the absolute or relative error doesn't exceed 10 - 6. 

Examples

Input

3
0 0
1 0
2 1


Output

3.650281539872885


Input

4
0 0
1 0
2 1
2 0


Output

-1

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
const double pi = acos(0.0) * 2.0;
const double eps = 1e-12;
const int step[4][2] = {{1, 0}, {-1, 0}, {0, 1}, {0, -1}};
template <class T>
inline T abs1(T a) {
  return a < 0 ? -a : a;
}
template <class T>
inline T max1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a > b ? a : b;
  if (c != -1234567) ans = max1(ans, c);
  if (d != -1234567) ans = max1(ans, d);
  return ans;
}
template <class T>
inline T min1(T a, T b, T c = -1234567, T d = -1234567) {
  T ans = a < b ? a : b;
  if (c != -1234567) ans = min(ans, c);
  if (d != -1234567) ans = min(ans, d);
  return ans;
}
template <class T>
inline T gcd1(T a, T b) {
  if (a < b) swap(a, b);
  if (a % b == 0) return b;
  return gcd1(b, a % b);
}
template <class T>
inline T lb(T num) {
  return num & (-num);
}
inline int jud(double a, double b) {
  if (abs1(a - b) < eps) return 0;
  if (a < b) return -1;
  return 1;
}
template <class t>
inline int find(t val, t* a, int na, bool f_small = 1, bool f_lb = 1) {
  if (na == 1) return 0;
  int be = 0, en = na - 1;
  if (a[0] <= a[na - 1]) {
    if (f_lb == 0)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(a[mid], val) != 1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(a[mid], val) != -1)
          en = mid;
        else
          be = mid + 1;
      }
    if (f_small && jud(a[be], val) == 1 && be != 0) be--;
    if (!f_small && jud(a[be], val) == -1 && be != na - 1) be++;
  } else {
    if (f_lb)
      while (be < en) {
        int mid = (be + en + 1) / 2;
        if (jud(a[mid], val) != -1)
          be = mid;
        else
          en = mid - 1;
      }
    else
      while (be < en) {
        int mid = (be + en) / 2;
        if (jud(a[mid], val) != 1)
          en = mid;
        else
          be = mid + 1;
      }
    if (!f_small && jud(a[be], val) == -1 && be != 0) be--;
    if (f_small && jud(a[be], val) == 1 && be != na - 1) be++;
  }
  return be;
}
inline int bitnum(unsigned long long nValue) {
  nValue = ((0xaaaaaaaaaaaaaaaaull & nValue) >> 1) +
           (0x5555555555555555ull & nValue);
  nValue = ((0xccccccccccccccccull & nValue) >> 2) +
           (0x3333333333333333ull & nValue);
  nValue = ((0xf0f0f0f0f0f0f0f0ull & nValue) >> 4) +
           (0x0f0f0f0f0f0f0f0full & nValue);
  nValue = ((0xff00ff00ff00ff00ull & nValue) >> 8) +
           (0x00ff00ff00ff00ffull & nValue);
  nValue = ((0xffff0000ffff0000ull & nValue) >> 16) +
           (0x0000ffff0000ffffull & nValue);
  nValue = ((0xffffffff00000000ull & nValue) >> 32) +
           (0x00000000ffffffffull & nValue);
  return nValue;
}
long long pow(long long n, long long m, long long mod = 0) {
  long long ans = 1;
  long long k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (mod) ans %= mod;
    }
    k *= k;
    if (mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
template <int MAXN, typename T = int, typename S = T>
struct MinCostMaxFlow {
  struct NegativeCostCircuitExistsException {};
  struct Edge {
    int v;
    T c;
    S w;
    int b;
    Edge(int v, T c, S w, int b) : v(v), c(c), w(w), b(b) {}
  };
  int n, source, sink;
  vector<Edge> e[MAXN];
  void init(int n, int source, int sink) {
    this->n = n;
    this->source = source;
    this->sink = sink;
    for (int i = 0; i < n; ++i) {
      e[i].clear();
    }
  }
  void addEdge(int a, int b, T c, S w) {
    e[a].push_back(Edge(b, c, w, e[b].size()));
    e[b].push_back(Edge(a, 0, -w, e[a].size() - 1));
  }
  bool mark[MAXN];
  T maxc[MAXN];
  S minw[MAXN];
  int dist[MAXN];
  Edge* prev[MAXN];
  bool _spfa() {
    queue<int> q;
    fill(mark, mark + n, false);
    fill(maxc, maxc + n, 0);
    fill(minw, minw + n, numeric_limits<S>::max());
    fill(dist, dist + n, 0);
    fill(prev, prev + n, (Edge*)NULL);
    mark[source] = true;
    maxc[source] = numeric_limits<T>::max();
    minw[source] = 0;
    q.push(source);
    while (!q.empty()) {
      int cur = q.front();
      mark[cur] = false;
      q.pop();
      for (typename vector<Edge>::iterator it = e[cur].begin();
           it != e[cur].end(); ++it) {
        T c = min(maxc[cur], it->c);
        if (c == 0) {
          continue;
        }
        int v = it->v;
        S w = minw[cur] + it->w;
        if (minw[v] > w + eps || (fabs(minw[v] - w) < eps && maxc[v] < c)) {
          maxc[v] = c;
          minw[v] = w;
          dist[v] = dist[cur] + 1;
          if (dist[v] >= n) {
            return false;
          }
          prev[v] = &*it;
          if (!mark[v]) {
            mark[v] = true;
            q.push(v);
          }
        }
      }
    }
    return true;
  }
  pair<T, S> gao() {
    T sumc = 0;
    S sumw = 0;
    while (true) {
      if (!_spfa()) {
        throw NegativeCostCircuitExistsException();
      } else if (maxc[sink] == 0) {
        break;
      } else {
        T c = maxc[sink];
        sumc += c;
        sumw += c * minw[sink];
        int cur = sink;
        while (cur != source) {
          Edge* e1 = prev[cur];
          e1->c -= c;
          Edge* e2 = &e[e1->v][e1->b];
          e2->c += c;
          cur = e2->v;
        }
      }
    }
    return make_pair(sumc, sumw);
  }
};
const int MAXN = 1010;
MinCostMaxFlow<MAXN, int, double> g;
const int maxn = 500;
struct node {
  int x, y;
  bool operator<(const node& a) const { return y > a.y; }
} orig[maxn];
int n;
long double dis(int x1, int y1, int x2, int y2) {
  return sqrt((x1 - x2) * (x1 - x2) + (y1 - y2) * (y1 - y2));
}
int main() {
  scanf("%d", &n);
  for (int j = 0; j < n; j++) scanf("%d%d", &orig[j].x, &orig[j].y);
  sort(orig, orig + n);
  if (orig[0].y <= orig[1].y) {
    cout << -1 << endl;
    return 0;
  }
  g.init(n * 2 + 2, 0, 2 * n + 1);
  for (int i = 1; i < n; i++) g.addEdge(0, i + 1, 1, 0);
  for (int i = 1; i < n; i++)
    for (int j = 0; j < i; j++)
      if (orig[j].y > orig[i].y)
        g.addEdge(i + 1, j + n + 1, 1,
                  dis(orig[i].x, orig[i].y, orig[j].x, orig[j].y));
  for (int i = 0; i < n; i++) g.addEdge(i + n + 1, n * 2 + 1, 2, 0);
  pair<int, double> ans = g.gao();
  if (ans.first != n - 1) {
    cout << -1 << endl;
    return 0;
  }
  cout << fixed << setprecision(15) << ans.second << endl;
  return 0;
}

```