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;

#define REP(i, n) for (int i=0; i<(n); ++i)
#define RREP(i, n) for (int i=(int)(n)-1; i>=0; --i)
#define FOR(i, a, n) for (int i=(a); i<(n); ++i)
#define RFOR(i, a, n) for (int i=(int)(n)-1; i>=(a); --i)

#define SZ(x) ((int)(x).size())
#define ALL(x) (x).begin(),(x).end()

#define DUMP(x) cerr<<#x<<" = "<<(x)<<endl
#define DEBUG(x) cerr<<#x<<" = "<<(x)<<" (L"<<__LINE__<<")"<<endl;

template<class T>
ostream &operator<<(ostream &os, const vector <T> &v) {
    os << "[";
    REP(i, SZ(v)) {
        if (i) os << ", ";
        os << v[i];
    }
    return os << "]";
}

template<class T, class U>
ostream &operator<<(ostream &os, const pair <T, U> &p) {
    return os << "(" << p.first << " " << p.second << ")";
}

template<class T>
bool chmax(T &a, const T &b) {
    if (a < b) {
        a = b;
        return true;
    }
    return false;
}

template<class T>
bool chmin(T &a, const T &b) {
    if (b < a) {
        a = b;
        return true;
    }
    return false;
}

using ll = long long;
using ull = unsigned long long;
using ld = long double;
using P = pair<int, int>;
using vi = vector<int>;
using vll = vector<ll>;
using vvi = vector<vi>;
using vvll = vector<vll>;

const ll MOD = 1e9 + 7;
const int INF = INT_MAX / 2;
const ll LINF = LLONG_MAX / 2;
const ld eps = 1e-9;


// template {{{

using Real = double;
const Real PI = acos(-1);

using Point = complex<Real>;
namespace std {
    bool operator<(const Point& a, const Point& b) {
        if (a.real() == b.real()) return a.imag() < b.imag();
        return a.real() < b.real();
    }
}

struct Line {
    Point a, b;
    Line() {}
    Line(const Point& a, const Point& b) : a(a), b(b) {}
    friend ostream& operator<<(ostream& os, const Line& l) {
        return os << "[" << l.a << "," << l.b << "]";
    }
};

struct Segment : Line {
    Segment() {}
    // Segment() = default;

    Segment(const Point& a, const Point& b) : Line(a, b) {}
};

inline bool eq(Real a, Real b) { return abs(b - a) < eps; }

// }}}


// utils {{{

Real radian_to_degree(Real r) {
    return r * 180.0 / PI;
}

Real degree_to_radian(Real d) {
    return d * PI / 180.0;
}

Point rotate(const Point &p, Real theta) {
    return p * polar((Real)1.0, theta);
}

Real cross(const Point& a, const Point& b) {
    return a.real() * b.imag() - a.imag() * b.real();
}

Real dot(const Point& a, const Point& b) {
    return a.real() * b.real() + a.imag() * b.imag();
}

// }}}


/**
* @brief 点p の直線l への射影を求める.
*/
Point projection(const Line& l, const Point& p) {
    Real A = dot(l.b - l.a, p - l.a),
            B = dot(l.a - l.b, p - l.b);
    return (A * l.b + B * l.a) / (A + B);
}

/**
* @brief 2直線の並行判定
*/
bool parallel(const Line& l1, const Line& l2) {
    return eq(cross(l1.a - l1.b, l2.a - l2.b), 0.0);
}

/**
* @brief 2直線の直行判定
*/
bool orthogonal(const Line& l1, const Line& l2) {
    return eq(dot(l1.a - l1.b, l2.a - l2.b), 0.0);
}


/**
* @brief 有向線分と点の位置関係
* @param[in] a, b, c: 線分a->b, 点c
* @return 線分a->b からみて, 点c がどこにあるか.
*/
const int COUNTER_CLOCKWISE = 1,
        CLOCKWISE = -1,
        ONLINE_BACK = 2,
        ONLINE_FRONT = -2,
        ON_SEGMENT = 0,
        ONEDGE_BACK = 3,
        ONEDGE_FRONT = -3;
int ccw(const Point& a, Point b, Point c) {
    b = b - a, c = c - a;
    if (cross(b, c) > eps) return COUNTER_CLOCKWISE;
    if (cross(b, c) < -eps) return CLOCKWISE;
    if (dot(b, c) < -eps) return ONLINE_BACK;
    if (norm(b) + eps < norm(c)) return ONLINE_FRONT;
    if (norm(c) < eps) return ONEDGE_BACK;
    if (abs(norm(b) - norm(c)) < eps) return ONEDGE_FRONT;
    return ON_SEGMENT;
}


// 交差 {{{

/**
* @brief 直線と点の交差判定
*/
bool intersected(const Line& l, const Point& p) {
    return abs(ccw(l.a, l.b, p)) != 1;
}

/**
* @brief 線分と点の交差判定
*/
bool intersected(const Segment& s, const Point& p) {
    return ccw(s.a, s.b, p) == 0;
}

/**
* @brief 直線と線分の交差判定
*/
bool intersected(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;
}

/**
* @brief 2つの線分の交差判定
*/
bool intersected(const Segment& s1, const Segment& s2) {
    return ccw(s1.a, s1.b, s2.a) * ccw(s1.a, s1.b, s2.b) <= 0 and
           ccw(s2.a, s2.b, s1.a) * ccw(s2.a, s2.b, s1.b) <= 0;
}


/**
* @brief 2直線の交点
*/
Point crosspoint(const Line& l1, const Line& l2) {
    Real A = cross(l2.a - l1.a, l2.b - l1.a),
            B = cross(l2.b - l1.b, l2.a - l1.b);
    return (A * l1.b + B * l1.a) / (A + B);
}

// }}}


// 距離 {{{

/**
* @brief 直線と点の距離
*/
Real distance(const Line& l, const Point& p) {
    return abs(p - projection(l, p));
}

/**
* @brief 線分と点の距離
*/
Real distance(const Segment& s, const Point& p) {
    Point r = projection(s, p);
    if (intersected(s, r)) return abs(r - p);
    return min(abs(s.a - p), abs(s.b - p));
}

/**
* @brief 直線と線分の距離
*/
Real distance(const Line &l, const Segment &s) {
    if (intersected(l, s)) return 0;
    return min(distance(l, s.a), distance(l, s.b));
}

/**
* @brief 2つの線分の距離
*/
Real distance(const Segment& s1, const Segment& s2) {
    if (intersected(s1, s2)) return 0.0;
    return min({ distance(s1, s2.a), distance(s1, s2.b),
                 distance(s2, s1.a), distance(s2, s1.b) });
}

// }}}


int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(10);


    // ifstream in("in.txt");
    // cin.rdbuf(in.rdbuf());

    for (;;) {
        int n; cin >> n;
        if (n == 0) break;
        map<string, vector<Segment>> segments;
        REP(i, n) {
            string country; cin >> country;
            vector<Point> p;
            for (;;) {
                int x; cin >> x;
                if (x == -1) break;
                int y; cin >> y;
                p.emplace_back((double)x, (double)y);
            }
            int m = p.size();
            REP(j, m) {
                segments[country].emplace_back(p[j], p[(j+1) % m]);
            }
        }
        map<string,int> ord;
        for (auto &tp : segments) {
            ord[tp.first] = -1;
        }
        int cnt = 0;
        for (auto &tp : ord) {
            tp.second = cnt++;
        }
        vvi G(cnt, vi(cnt));
        for (auto &tp1 : segments) {
            for (auto &tp2 : segments) {
                if (tp1.first == tp2.first) continue;
                for (const Segment &s1 : tp1.second) {
                    for (const Segment &s2 : tp2.second) {
                        if (intersected(s1, s2)) {
                            G[ord[tp1.first]][ord[tp2.first]] = 1;
                        }
                    }
                }
            }
        }

        vi color(cnt, -1);
        function<int(int,int)> dfs = [&](int i, int upper) {
            if (i == cnt) {
                return upper;
            }
            int ret = 10;
            REP(c, upper+1) {
                bool valid = true;
                REP(j, i) {
                    if (G[i][j] and c == color[j]) {
                        valid = false;
                        break;
                    }
                }
                if (valid) {
                    color[i] = c;
                    chmin(ret, dfs(i+1, max(upper, c+1)));
                    color[i] = -1;
                }
            }
            return ret;
        };

        int ans = dfs(0, 0);
        cout << ans << endl;
    }

    return 0;
}

