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>
#pragma GCC optimize("O3,unroll-loops")
#pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
//mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
//ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+7;

struct state
{
    vector<bool> del;
    vi set_num;
    int cur_max;
    ll hash()
    {
        ll h = cur_max;
        ll h2 = cur_max;
        ll p = 2137;
        ll p2 = 2137001;
        rep(i,siz(del))
        {
            h = (h+(ll)del[i]*p)%MOD;
            h2 = (h2+(ll)del[i]*p2)%MOD;
            p = (p*2137)%MOD;
            p2 = (p2*2137001)%MOD;
        }
        rep(i,siz(set_num))
        {
            h = (h+(ll)(set_num[i]+1)*p)%MOD;
            h2 = (h2+(ll)(set_num[i]+1)*p2)%MOD;
            p = (p*2137)%MOD;
            p2 = (p2*2137001)%MOD;
        }
        return h+h2*MOD;
    }
};

int n;
vi graph[1001];
unordered_map<ll,vi> ans_map;

vi rek(state s)
{
    ll h = s.hash();
    if(ans_map.find(h) != ans_map.end()) return ans_map[h];
    int ile = 0;
    rep(i,n) if(s.del[i] == 0) ile++;
    if(ile <= 2)
    {
        ans_map[h] = {};
        return ans_map[h];
    }
    // set leaf
    pii min_ = {1e9,-1};
    rep(i,n)
    {
        if(s.del[i] == 1 || s.set_num[i] == -1) continue;
        int cnt = 0;
        forall(it,graph[i]) if(!s.del[it]) cnt++;
        if(cnt == 1) min_ = min(min_,{s.set_num[i],i});
    }
    if(min_.ss != -1)
    {
        int v = 0;
        forall(it,graph[min_.ss]) if(!s.del[it]) v = it;
        if(s.set_num[v] == -1)
        {
            s.set_num[v] = s.cur_max;
            s.cur_max++;
            s.del[min_.ss] = 1;
            ans_map[h] = {s.cur_max-1};
            vi pom = rek(s);
            forall(it,pom) ans_map[h].pb(it);
            return ans_map[h];
        } 
        else
        {
            s.del[min_.ss] = 1;
            ans_map[h] = {s.set_num[v]};
            vi pom = rek(s);
            forall(it,pom) ans_map[h].pb(it);
            return ans_map[h];
        }
    }
    // set hub
    min_ = {1e9,-1};
    rep(i,n)
    {
        if(s.del[i] == 1 || s.set_num[i] == -1) continue;
        int cnt = 0;
        forall(it,graph[i])
        {
            if(!s.del[it])
            {
                int cnt2 = 0;
                forall(it2,graph[it])
                {
                    if(!s.del[it2])
                    {
                        cnt2++;
                        if(cnt2 == 2) break;
                    }
                }
                if(cnt2 <= 1) 
                {
                    cnt++;
                    break;
                }
            }
        }
        if(cnt >= 1) min_ = min(min_,{s.set_num[i],i});
    }
    if(min_.ss != -1)
    {
        forall(it,graph[min_.ss])
        {
            if(!s.del[it])
            {
                int cnt2 = 0;
                forall(it2,graph[it])
                {
                    if(!s.del[it2])
                    {
                        cnt2++;
                        if(cnt2 == 2) break;
                    }
                }
                if(cnt2 <= 1)
                {
                    if(ile != 2)
                    {
                        ans_map[h].pb(s.set_num[min_.ss]);
                        s.del[it] = 1;
                    }
                    ile--;
                }
            }
        }
        vi pom = rek(s);
        forall(it,pom) ans_map[h].pb(it);
        return ans_map[h];
    }
    // rand hub
    rep(i,n)
    {
        if(s.del[i] == 1) continue;
        int cnt = 0;
        forall(it,graph[i])
        {
            if(!s.del[it])
            {
                int cnt2 = 0;
                forall(it2,graph[it])
                {
                    if(!s.del[it2])
                    {
                        cnt2++;
                        if(cnt2 == 2) break;
                    }
                }
                if(cnt2 <= 1) 
                {
                    cnt++;
                    break;
                }
            }
        }
        if(cnt == 0) continue;
        s.set_num[i] = s.cur_max;
        s.cur_max++;
        if(ans_map.find(h) == ans_map.end()) ans_map[h] = rek(s);
        else ans_map[h] = min(ans_map[h],rek(s));
        s.set_num[i] = -1;
        s.cur_max--;
    }
    return ans_map[h];
}

void solve()
{
    cin >> n;
    rep(i,n) graph[i] = {};
    ans_map = {};
    rep(i,n-1)
    {
        int a,b;
        cin >> a >> b;
        a--;
        b--;
        graph[a].pb(b);
        graph[b].pb(a);
    }
    state s;
    s.del.resize(n,0);
    s.set_num.resize(n,-1);
    s.cur_max = 1;
    vi ans = rek(s);
    forall(it,ans) cout << it << " ";
    cout << "\n";
}

int main()
{
    ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0);
    //random_start();
    int t = 1;
    cin >> t;
    while(t--) solve();
}