You were lucky enough to get a map just before entering the legendary magical mystery world. The map shows the whole area of your planned exploration, including several countries with complicated borders. The map is clearly drawn, but in sepia ink only; it is hard to recognize at a glance which region belongs to which country, and this might bring you into severe danger. You have decided to color the map before entering the area. “A good deal depends on preparation,” you talked to yourself.

Each country has one or more territories, each of which has a polygonal shape. Territories belonging to one country may or may not “touch” each other, i.e. there may be disconnected territories. All the territories belonging to the same country must be assigned the same color. You can assign the same color to more than one country, but, to avoid confusion, two countries “adjacent” to each other should be assigned different colors. Two countries are considered to be “adjacent” if any of their territories share a border of non-zero length.

Write a program that finds the least number of colors required to color the map.



Input

The input consists of multiple map data. Each map data starts with a line containing the total number of territories n, followed by the data for those territories. n is a positive integer not more than 100. The data for a territory with m vertices has the following format:


String
x1 y1
x2 y2
...
xm ym
-1


“String” (a sequence of alphanumerical characters) gives the name of the country it belongs to. A country name has at least one character and never has more than twenty. When a country has multiple territories, its name appears in each of them.

Remaining lines represent the vertices of the territory. A vertex data line has a pair of nonneg- ative integers which represent the x- and y-coordinates of a vertex. x- and y-coordinates are separated by a single space, and y-coordinate is immediately followed by a newline. Edges of the territory are obtained by connecting vertices given in two adjacent vertex data lines, and byconnecting vertices given in the last and the first vertex data lines. None of x- and y-coordinates exceeds 1000. Finally, -1 in a line marks the end of vertex data lines. The number of vertices m does not exceed 100.

You may assume that the contours of polygons are simple, i.e. they do not cross nor touch themselves. No two polygons share a region of non-zero area. The number of countries in a map does not exceed 10.

The last map data is followed by a line containing only a zero, marking the end of the input data.

Output

For each map data, output one line containing the least possible number of colors required to color the map satisfying the specified conditions.

Example

Input

6
Blizid
0 0
60 0
60 60
0 60
0 50
50 50
50 10
0 10
-1
Blizid
0 10
10 10
10 50
0 50
-1
Windom
10 10
50 10
40 20
20 20
20 40
10 50
-1
Accent
50 10
50 50
35 50
35 25
-1
Pilot
35 25
35 50
10 50
-1
Blizid
20 20
40 20
20 40
-1
4
A1234567890123456789
0 0
0 100
100 100
100 0
-1
B1234567890123456789
100 100
100 200
200 200
200 100
-1
C1234567890123456789
0 100
100 100
100 200
0 200
-1
D123456789012345678
100 0
100 100
200 100
200 0
-1
0


Output

4
2
#include <bits/stdc++.h>

using namespace std;

const int mod = 1e9 + 7;

template< typename T = long long >
T pow_mod(T x, T n, T mod)
{
  T ret = 1;
  while(n > 0) {
    if(n & 1) ret = 1LL * ret * x % mod;
    x = 1LL * x * x % mod;
    n >>= 1;
  }
  return ret;
}

const double EPS = 1e-8, PI = acos(-1);

inline bool eq(double a, double b) { return abs(b - a) < EPS; }

#define curr(P, i) P[i]
#define next(P, i) P[(i+1)%P.size()]
#define prev(P, i) P[(i+P.size()-1) % P.size()]
enum
{
  OUT, ON, IN
};
namespace Geometory
{
  struct Point
  {
    double x, y;

    Point() {};

    Point(double x, double y) : x(x), y(y) {};

    Point operator+(const Point &b) const { return Point(x + b.x, y + b.y); }

    Point operator-(const Point &b) const { return Point(x - b.x, y - b.y); }

    Point operator*(const double b) const { return Point(x * b, y * b); }

    Point operator*(const Point &b) const { return Point(x * b.x - y * b.y, x * b.y + y * b.x); }

    Point operator/(const double b) const { return Point(x / b, y / b); }

    bool operator<(const Point &b) const { return x != b.x ? x < b.x : y < b.y; }

    bool operator==(const Point &b) const { return eq(x, b.x) && eq(y, b.y); }

    double norm() { return x * x + y * y; }

    double arg() { return atan2(x, y); }

    double abs() { return sqrt(norm()); }

    Point rotate(double theta) { return Point(cos(theta) * x - sin(theta) * y, sin(theta) * x + cos(theta) * y); }

    Point rotate90() { return Point(-y, x); }

    friend ostream &operator<<(ostream &os, Point &p) { return os << "(" << p.x << "," << p.y << ")"; }

    friend istream &operator>>(istream &is, Point &a) { return is >> a.x >> a.y; }
  };

  struct Line
  {
    Point a, b;

    Line() {};

    Line(Point a, Point b) : a(a), b(b) {};

    friend ostream &operator<<(ostream &os, Line &p) { return os << "(" << p.a.x << "," << p.a.y << ") to (" << p.b.x << "," << p.b.y << ")"; }

    friend istream &operator>>(istream &is, Line &a) { return is >> a.a.x >> a.a.y >> a.b.x >> a.b.y; }
  };

  struct Segment
  {
    Point a, b;

    Segment() {};

    Segment(Point a, Point b) : a(a), b(b) {};

    friend ostream &operator<<(ostream &os, Segment &p) { return os << "(" << p.a.x << "," << p.a.y << ") to (" << p.b.x << "," << p.b.y << ")"; }

    friend istream &operator>>(istream &is, Segment &a) { return is >> a.a.x >> a.a.y >> a.b.x >> a.b.y; }
  };

  struct Circle
  {
    Point p;
    double r;

    Circle() {};

    Circle(Point p, double r) : p(p), r(r) {};
  };

  typedef vector< Point > Polygon;
  typedef vector< Segment > Segments;
  typedef vector< Line > Lines;
  typedef vector< Circle > Circles;
  typedef pair< Point, Point > PointPoint;

  double cross(const Point &a, const Point &b)
  {
    return a.x * b.y - a.y * b.x;
  }

  double dot(const Point &a, const Point &b)
  {
    return a.x * b.x + a.y * b.y;
  }

  int ccw(const Point &a, Point b, Point c)
  {
    b = b - a, c = c - a;
    if(cross(b, c) > 0) return +1;
    if(cross(b, c) < 0) return -1;
    if(dot(b, c) <= 0) return +2;
    if(b.norm() <= c.norm()) return -2;
    return 0;
  }

  Point Projection(const Line &l, const Point &p)
  {
    double t = dot(p - l.a, l.a - l.b) / (l.a - l.b).norm();
    return l.a + (l.a - l.b) * t;
  }

  Point Projection(const Segment &l, const Point &p)
  {
    double t = dot(p - l.a, l.a - l.b) / (l.a - l.b).norm();
    return l.a + (l.a - l.b) * t;
  }

  Point Reflection(const Line &l, const Point &p)
  {
    return p + (Projection(l, p) - p) * 2.0;
  }

  double Distance(const Line &l, const Point &p)
  { //OK
    return (p - Projection(l, p)).abs();
  }

  bool Intersect(const Line &l, const Line &m)
  {
    return abs(cross(l.b - l.a, m.b - m.a)) > EPS || abs(cross(l.b - l.a, m.b - l.a)) < EPS;
  }

  bool Intersect(const Line &l, const Segment &s)
  {
    return cross(l.b - l.a, s.a - l.a) * cross(l.b - l.a, s.b - l.a) < EPS;
  }

  bool Intersect(const Line &l, const Point &p)
  {
    return abs(ccw(l.a, l.b, p)) != -1;
  }

  bool Intersect(const Segment &s, const Segment &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 Intersect(const Segment &s, const Point &p)
  {
    return ccw(s.a, s.b, p) == 0;
  }

  bool Intersect(const Circle &c, const Line &l)
  {
    return Distance(l, c.p) <= c.r + EPS;
  }

  bool Intersect(const Circle &c, const Point &p)
  {
    return abs((p - c.p).abs() - c.r) < EPS;
  }

  int Intersect(const Circle &c, const Segment &l)
  {
    if((Projection(l, c.p) - c.p).norm() - c.r * c.r > EPS) return 0;
    const double d1 = (c.p - l.a).abs(), d2 = (c.p - l.b).abs();
    if(d1 < c.r + EPS && d2 < c.r + EPS) return 0;
    if(d1 < c.r - EPS && d2 > c.r + EPS || d1 > c.r + EPS && d2 < c.r - EPS) return 1;
    const Point h = Projection(l, c.p);
    if(dot(l.a - h, l.b - h) < 0) return 2;
    return 0;
  }

  bool Intersect(const Circle &a, const Circle &b)
  {
    return ((a.p - b.p).norm() - (a.r + b.r) * (a.r + b.r) < EPS) &&
           ((a.p - b.p).norm() - (a.r - b.r) * (a.r - b.r) > -EPS);
  }

  double Distance(const Segment &s, const Point &p)
  {
    Point r = Projection(s, p);
    if(Intersect(s, r)) return (r - p).abs();
    return min((s.a - p).abs(), (s.b - p).abs());
  }

  double Distance(const Segment &a, const Segment &b)
  {
    if(Intersect(a, b)) return 0;
    return min(min(Distance(a, b.a), Distance(a, b.b)), min(Distance(b, a.a), Distance(b, a.b)));
  }

  double Distance(const Line &l, const Line &m)
  {
    return Intersect(l, m) ? 0 : Distance(l, m.a);
  }

  double Distance(const Line &l, const Segment &s)
  { //OK
    if(Intersect(l, s)) return 0;
    return min(Distance(l, s.a), Distance(l, s.b));
  }

  double Distance(const Point &a, const Point &b)
  { //OK
    return (a - b).abs();
  }

  Point Crosspoint(const Segment &l, const Segment &m)
  { //OK
    double A = cross(l.b - l.a, m.b - m.a);
    double B = cross(l.b - l.a, l.b - m.a);
    if(abs(A) < EPS && abs(B) < EPS) return m.a; // same line
    return m.a + (m.b - m.a) * B / A;
  }

  PointPoint Crosspoint(const Circle &c, const Line l)
  {
    Point hp = Projection(l, c.p), h = hp - c.p;
    const double d2 = h.norm();
    Point v = (l.b - l.a) * sqrt(c.r * c.r - d2) / (l.b - l.a).abs();
    return PointPoint(hp - v, hp + v);
  }

  PointPoint Crosspoint(const Circle &c, const Segment &l)
  {
    Line aa = Line(l.a, l.b);
    if(Intersect(c, l) == 2) return Crosspoint(c, aa);
    PointPoint ret = Crosspoint(c, aa);
    if(dot(l.a - ret.first, l.b - ret.first) < 0) ret.second = ret.first;
    else ret.first = ret.second;
    return ret;
  }

  PointPoint Crosspoint(const Circle &c1, const Circle &c2)
  { //OK
    double d = (c1.p - c2.p).abs();
    double s = (c1.r + c2.r + d) / 2;
    double S = sqrt(s * (s - c1.r) * (s - c2.r) * (s - d));
    double h = 2 * S / d;
    Point v = (c2.p - c1.p) / (c2.p - c1.p).abs();
    double m = sqrt(c1.r * c1.r - h * h);
    return PointPoint(c1.p + v * m + Point(0, 1) * h * v, c1.p + v * m - Point(0, 1) * h * v);
  }

  bool parallel(const Line &a, const Line &b)
  {
    return abs(cross(a.b - a.a, b.b - b.a)) < EPS;
  }

  bool orthogonal(const Line &a, const Line &b)
  {
    return abs(dot(a.a - a.b, b.a - b.b)) < EPS;
  }

  int Contains(const Polygon &Q, const Point &p)
  {
    bool in = false;
    for(int i = 0; i < Q.size(); i++) {
      Point a = curr(Q, i) - p, b = next(Q, i) - p;
      if(a.y > b.y) swap(a, b);
      if(a.y <= 0 && 0 < b.y && cross(a, b) < 0) in = !in;
      if(cross(a, b) == 0 && dot(a, b) <= 0) return ON;
    }
    return in ? IN : OUT;
  }

  bool Contains(const Circle &c, const Point &p)
  {
    return (c.p - p).abs() < c.r + EPS;
  }

  double Area2(const Polygon &p)
  { //OK
    double A = 0;
    for(int i = 0; i < p.size(); ++i) {
      A += cross(curr(p, i), next(p, i));
    }
    return A;
  }

  bool IsConvex(const Polygon &p)
  {
    for(int i = 0; i < p.size(); i++) {
      if(ccw(prev(p, i), curr(p, i), next(p, i)) == -1) return false;
    }
    return true;
  }

  Polygon Convex_Hull(Polygon &p)
  {
    int n = p.size(), k = 0;
    if(n >= 3) {
      sort(p.begin(), p.end());
      vector< Point > ch(2 * n);
      for(int i = 0; i < n; ch[k++] = p[i++]) {
        while(k >= 2 && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
      }
      for(int i = n - 2, t = k + 1; i >= 0; ch[k++] = p[i--]) {
        while(k >= t && cross(ch[k - 1] - ch[k - 2], p[i] - ch[k - 1]) < 0) --k;
      }
      ch.resize(k - 1);
      return ch;
    } else {
      return p;
    }
  }

  double Convex_Diameter(Polygon &p)
  {
    int n = p.size();
    int is = 0, js = 0;
    for(int i = 1; i < n; i++) {
      if(p[i].y > p[is].y) is = i;
      if(p[i].y < p[js].y) js = i;
    }
    double maxdis = (p[is] - p[js]).norm();

    int maxi, maxj, i, j;
    i = maxi = is;
    j = maxj = js;
    do {
      if(cross(next(p, i) - curr(p, i), next(p, j) - curr(p, j)) >= 0) {
        j = (j + 1) % n;
      } else {
        i = (i + 1) % n;
      }
      if((p[i] - p[j]).norm() > maxdis) {
        maxdis = (p[i] - p[j]).norm();
        maxi = i;
        maxj = j;
      }
    } while(i != is || j != js);
    return maxdis;
  }
};

using namespace Geometory;

int main()
{
  int N;
  while(cin >> N, N) {
    map< string, vector< Polygon > > data;
    vector< string > nums;
    for(int i = 0; i < N; i++) {
      string S;
      cin >> S;
      int x, y;
      Polygon polygon;
      while(cin >> x, ~x) {
        cin >> y;
        polygon.push_back(Point(x, y));
      }

      nums.push_back(S);
      data[S].push_back(polygon);
    }

    sort(begin(nums), end(nums));
    nums.erase(unique(begin(nums), end(nums)), end(nums));

    int sz = (int) nums.size(), g[10][10] = {{}};
    for(auto &ps : data) {
      for(auto &qs : data) {
        if(ps.first == qs.first) continue;
        int u = lower_bound(begin(nums), end(nums), ps.first) - begin(nums);
        int v = lower_bound(begin(nums), end(nums), qs.first) - begin(nums);
        bool crossed = false;
        for(auto &p : ps.second) {
          for(auto &q : qs.second) {
            for(int i = 0; i < p.size(); i++) {
              for(int j = 0; j < q.size(); j++) {
                if(Intersect(Segment(curr(p, i), next(p, i)), Segment(curr(q, j), next(q, j)))) {
                  crossed = true;
                }
              }
            }
          }
        }
        g[u][v] = crossed;
      }
    }


    vector< int > beet;
    for(int i = 0; i < 1 << sz; i++) {
      bool flag = true;
      for(int j = 0; j < sz; j++) {
        for(int k = 0; k < j; k++) {
          if((i >> j) & 1 && (i >> k) & 1 && g[j][k]) flag = false;
        }
      }
      if(flag) beet.push_back(i);
    }

    vector< int > dp(1 << sz, sz);
    dp[0] = 0;
    for(int i = 0; i < 1 << sz; i++) {
      for(auto &j : beet) dp[i | j] = min(dp[i | j], dp[i] + 1);
    }
    cout << dp.back() << endl;
  }
}