1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
#include "bits/stdc++.h"
using namespace std;

struct xyi {
    int x;
    int y;
    int i;
};

struct Points {
    vector<xyi> xy;
    vector<xyi> yx;
    vector<xyi> dx;
};


ostream& operator<<(ostream& out, const xyi& p) {
    out << "(" << p.x << "," << p.y << ")@" << p.i;
    return out;
}

struct XYCmp {
    bool operator()(const xyi& p, const xyi& q) {
        return make_pair(p.x, -p.y) < make_pair(q.x, -q.y);
    }
};


struct YXCmp {
    bool operator()(const xyi& p, const xyi& q) {
        return make_pair(p.y, -p.x) < make_pair(q.y, -q.x);
    }
};

struct DXCmp {
    bool operator()(const xyi& p, const xyi& q) {
        return make_pair(p.x - p.y, p.x) < make_pair(q.x - q.y, q.x);
    }
};

template<int xyi::*X, int xyi::*Y>
xyi DecY(xyi p) {
    (p.*Y) = p.*Y - 1;;
    return p;
}
template<class T>
struct List {
    List():values(1), nxt(1, 0), prv(1,0){}
    vector<T> values;
    vector<int> nxt;
    vector<int> prv;
    void Insert(const T& what, int where=0) {
        int i = (int) values.size();
        values.push_back(what);
        nxt.push_back(where);
        prv.push_back(prv[where]);
        nxt[prv[where]] = i;
        prv[where] = i;
    }

    void Erase(int where) {
        nxt[prv[where]] = nxt[where];
        prv[nxt[where]] = prv[where];
        nxt[where] = prv[where] = -1;
    }

    int Size() {
        int sz = 0;
        for (int i = nxt[0]; i != 0; i = nxt[i]) {
            ++sz;
        }
        return sz;
    }
};

template<int xyi::*X = &xyi::x, int xyi::*Y = &xyi::y>
xyi MakeXyi(int x, int y) {
    xyi p;
    p.*X = x;
    p.*Y = y;
    p.i = -1;
    return p;
}

template<int xyi::*X, int xyi::*Y, vector<xyi> Points::*XY, class Cmp>
int FindA(const Points& ps, xyi p) {
    auto& xy = ps.*XY;
    auto jt = lower_bound(xy.begin(), xy.end(), DecY<X,Y>(p), Cmp());
    int x = -1;
    while (jt != xy.end()) {
        x = *jt.*X + (p.*Y - *jt.*Y);
        jt = lower_bound(xy.begin(), xy.end(),
                MakeXyi<X, Y>(x, (int)1e9), Cmp());
        if (jt != xy.end() && *jt.*X > x) {
            return 0;
        }
    }
    if (x == -1) {
        return 0;
    } else {
        return x - p.*X;
    }
}

bool HeuristicCheck(const Points& ps, int x0, int y0) {
    if (ps.xy.back().x >= x0 || ps.yx.back().y >= y0) {
        return false;
    }
    auto it = ps.dx.begin();

    int y = y0;
    while(true) {
        while (next(it) != ps.dx.end() && next(it)->x - next(it)->y <= x0 - y) ++it;
        if (it->x >= x0) return false;
        if (it->x - it->y == x0 - y) {
            y = it->y;
        } else {
            return ps.yx[0].y == y;
        }
    }

    return true;
}

bool ConsiderTopRight(const Points& ps, xyi p, vector<int>& as) {
    if (ps.xy.size() == 1) {
        as = vector<int>(1, 1);
        return true;
    }
    set<int> pas {
        FindA<&xyi::x, &xyi::y, &Points::xy, XYCmp>(ps, p),
        FindA<&xyi::y, &xyi::x, &Points::yx, YXCmp>(ps, p)};
    for (int a : pas) {
        if (a == -1) {
            as = vector<int>(1, 1);
            return true;
        }
        if (a == -2) {
            return false;
        }
    }

    for (int a0 : pas) {
        if (a0 <= 0) {continue;}
        int x0 = p.x + a0;
        int y0 = p.y + a0;
        if(!HeuristicCheck(ps, x0, y0)) {
            continue;
        }
        as = vector<int>(ps.xy.size(), -1);
        List<xyi> border;
        border.Insert(MakeXyi(x0,y0));
        unordered_set<int> active; active.insert(1);
        while (!active.empty()) {
            auto it = *active.begin(); active.erase(active.begin());
            int x = border.values[it].x;
            int y = border.values[it].y;
            auto jt = lower_bound(ps.dx.begin(), ps.dx.end(), MakeXyi(x, y), DXCmp());
            if (jt == ps.dx.begin() || prev(jt)->x - prev(jt)->y < x - y) {continue;}
            int a = x - prev(jt)->x;
            int ii = prev(jt)->i;
            if (a <= 0) {return false;}
            if ((it != border.nxt[0] && border.values[border.prv[it]].x > x - a) ||
                (border.nxt[it] != 0 && border.values[border.nxt[it]].y > y - a)) {
                continue;
            };
            as[ii] = a;
            if (it == border.nxt[0] || (it != border.nxt[0] && border.values[border.prv[it]].x < x - a)) {
                border.Insert(MakeXyi(x-a, y), it);
            }
            active.insert(border.prv[it]);
            if (border.nxt[it] == 0 || (border.nxt[it] != 0 && border.values[border.nxt[it]].y < y - a)) {
                border.Insert(MakeXyi(x, y-a), border.nxt[it]);
            }
            active.insert(border.nxt[it]);
            border.Erase(it);
        }
        if(border.Size() == 2 && find(as.begin(), as.end(), -1) == as.end()) {
            return true;
        }
    }
    return false;
}

int main() {
    ios_base::sync_with_stdio(false);
    int t;
    cin >> t;
    while (t--) {
        int n;
        cin >> n;
        Points ps;
        ps.xy.resize(n);
        for (int i = 0; i < n; ++i) {
            cin >> ps.xy[i].x >> ps.xy[i].y;
            ps.xy[i].i = i;
        }
        ps.yx = ps.dx = ps.xy;
        sort(ps.xy.begin(), ps.xy.end(), XYCmp{});
        sort(ps.yx.begin(), ps.yx.end(), YXCmp{});
        sort(ps.dx.begin(), ps.dx.end(), DXCmp{});

        vector<xyi> maxi;
        for (auto p : ps.xy) {
            while (!maxi.empty() && maxi.back().y <= p.y) {
                maxi.pop_back();
            }
            if (maxi.empty() || maxi.back().x < p.x) {
                maxi.push_back(p);
            }
        }
        bool found = false;
        vector<int> as;
        for(auto p : maxi) {
            if (ConsiderTopRight(ps, p, as)) {
                found = true;
                break;
            }
        }
        if (found) {
            cout << "TAK";
            for (int a : as) {
                cout << ' ' << a;
            }
                cout << '\n';
        } else {
            cout << "NIE\n";
        }
    }


}