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
#include <iostream>
#include <algorithm>
#include <vector>
#include <stack>
using namespace std;

#define LL long long
#define MAX_N 2010
#define INF 4001000000

int n;
pair<pair<LL, LL>, int> P[MAX_N];
pair<LL, LL> origin0;
pair<LL, LL> origin1;
LL S[MAX_N];
LL R[MAX_N];
vector<int> B;
vector<int> B1;
pair<LL, LL> bounds;

void clear() {
    B.clear();
    B1.clear();
}

LL maxSquare(int i) {
    LL ret = INF;
    for(int a = 0; a < n; ++a) {
        if(a != i) {
            if((P[a].first.first + S[a] > P[i].first.first && P[a].first.second > P[i].first.second) ||
                    (P[a].first.second + S[a] > P[i].first.second && P[a].first.first > P[i].first.first)) {
                ret = min(ret, max(P[a].first.second - P[i].first.second, P[a].first.first - P[i].first.first));
            }
        }
    }
    return ret;
}

pair<LL, LL> knownBounds() {
    LL right = 0, top = 0;
    for(int i : B1) {
        right = max(right, P[i].first.first + S[i]);
        top = max(top, P[i].first.second + S[i]);
    }
    if(right == P[B.back()].first.first) right = INF;
    if(top == P[B.front()].first.second) top = INF;
    return {right, top};
}

pair<bool, pair<LL, LL>> checkBCompletion(LL firstSize) {
    stack<pair<LL, LL>> stack;
    if(bounds.second != INF && bounds.second != P[B.front()].first.second + firstSize) {
        return {0, {0, 0}};
    }
    stack.push({INF, P[B.front()].first.second + firstSize});
    LL last = INF;
    for(int a = 0; a < int(B.size()); ++a) {
        auto p = P[B[a]].first;
        while(p.first >= stack.top().first) {
            if(p.first > stack.top().first) {
                return {0, {0, 0}};
            }
            stack.pop();
        }
        auto s = stack.top();
        LL d = s.second - p.second;
        if(p.first + d > s.first) {
            return {0, {0, 0}};
        }
        stack.push({p.first + d, p.second});
        last = p.first + d;
        S[B[a]] = d;
    }
    while(stack.size() > 1) {
        if(last != stack.top().first) {
            return {0, {0, 0}};
        }
        stack.pop();
    }
    if(bounds.first != INF && bounds.first != last) {
        return {0, {0, 0}};
    }
    return {1, {last, P[B.front()].first.second + firstSize}};
}

bool checkRectangle(LL right, LL top) {
    LL area = (right - origin0.first) * (top - origin0.second);
    LL sum = 0;
    for(int a = 0; a < n; ++a) {
        sum += S[a] * S[a];
    }
    return area == sum;
}

int main() {
    ios::sync_with_stdio(0);

    int tests;
    cin >> tests;
    while(tests--) {
        clear();

        cin >> n;
        LL left = INF, bottom = INF;
        for(int a = 0; a < n; ++a) {
            cin >> P[a].first.first >> P[a].first.second;
            P[a].second = a;
            left = min(left, P[a].first.first);
            bottom = min(bottom, P[a].first.second);
            S[a] = 1;
        }
        if(n == 1) {
            cout << "TAK 1\n";
            continue;
        }
        sort(P, P + n, [](const pair<pair<LL, LL>, int>& p1, const pair<pair<LL, LL>, int>& p2) {
            return make_pair(p1.first.second, p1.first.first) < make_pair(p2.first.second, p2.first.first);
        });
        origin0 = P[0].first;
        if(origin0.first != left || origin0.second != bottom) {
            cout << "NIE\n";
            continue;
        }

        for(int a = 0; a < n; ++a) {
            S[a] = maxSquare(a);
            if(S[a] == INF) {
                S[a] = 1;
            }
        }
        for(int a = 0; a < n; ++a) {
            S[a] = maxSquare(a);
            if(S[a] == INF) {
                S[a] = 1;
                B.push_back(a);
            } else {
                B1.push_back(a);
            }
        }
        std::reverse(B.begin(), B.end());
        std::reverse(B1.begin(), B1.end());

        origin1 = {P[B.front()].first.first, P[B.back()].first.second};

        bounds = knownBounds();

        bool isAnswer = 0;
        for(int a = 0; a <= int(B.size()); ++a) {
            LL firstSize;
            if(a == 0) firstSize = 1;
            else if(a < int(B.size())) firstSize = P[B[a]].first.first - origin1.first;
            else firstSize = P[B.back()].first.first - origin1.first + P[B.front()].first.second - origin1.second;
            auto r = checkBCompletion(firstSize);
            if(r.first) {
                if(checkRectangle(r.second.first, r.second.second)) {
                    for(int i = 0; i < n; ++i) {
                        R[P[i].second] = S[i];
                    }
                    cout << "TAK ";
                    for(int i = 0; i < n; ++i) {
                        cout << R[i] << " ";
                    }
                    cout << "\n";
                    isAnswer = 1;
                }
                break;
            }
        }

        if(!isAnswer) {
            cout << "NIE\n";
        }
    }
    return 0;
}