1 #include<cstdio>
2 #include<cstring>
3 #define MAXN 9
4 #define MAXH 800
5 #define MAXL 324
6 #define MAXM 240000
7 #define INF 0x7FFFFFFF
8 int size, cnt, a[MAXN][MAXN], sd[MAXN][MAXN], belong[MAXN][MAXN];
9 int L[MAXM], R[MAXM], U[MAXM], D[MAXM], C[MAXM], X[MAXM];
10 int S[MAXH], H[MAXH], Q[MAXH], ans[MAXL];
11 bool vis[MAXH];
12 void Dir(int x, int y, bool &up, bool &right, bool &down, bool &left)
13 {
14 sd[x][y] = a[x][y];
15 up = right = down = left = false;
16 if (sd[x][y] >= 128)
17 {
18 sd[x][y] -= 128;
19 left = true;
20 }
21 if (sd[x][y] >= 64)
22 {
23 sd[x][y] -= 64;
24 down = true;
25 }
26 if (sd[x][y] >= 32)
27 {
28 sd[x][y] -= 32;
29 right = true;
30 }
31 if (sd[x][y] >= 16)
32 {
33 sd[x][y] -= 16;
34 up = true;
35 }
36
37 }
38 void DFS(int x, int y, int color)
39 {
40 bool up, right, down, left;
41 belong[x][y] = color;
42 Dir(x, y, up, right, down, left);
43 if (!up && !belong[x - 1][y])
44 DFS(x - 1, y, color);
45 if (!down && !belong[x + 1][y])
46 DFS(x + 1, y, color);
47 if (!right && !belong[x][y + 1])
48 DFS(x, y + 1, color);
49 if (!left && !belong[x][y - 1])
50 DFS(x, y - 1, color);
51 }
52 void Init()
53 {
54 int i;
55 for (i = 0; i <= MAXL; i++)
56 {
57 L[i + 1] = i;
58 R[i] = i + 1;
59 U[i] = D[i] = i;
60 S[i] = 0;
61 }
62 R[MAXL] = 0;
63 size = MAXL + 1;
64 }
65 void Remove(int c)
66 {
67 int i, j;
68 L[R[c]] = L[c];
69 R[L[c]] = R[c];
70 for (i = D[c]; i != c; i = D[i])
71 {
72 for (j = R[i]; j != i; j = R[j])
73 {
74 U[D[j]] = U[j];
75 D[U[j]] = D[j];
76 S[C[j]]--;
77 }
78 }
79 }
80 void Resume(int c)
81 {
82 int i, j;
83 L[R[c]] = c;
84 R[L[c]] = c;
85 for (i = D[c]; i != c; i = D[i])
86 {
87 for (j = R[i]; j != i; j = R[j])
88 {
89 U[D[j]] = j;
90 D[U[j]] = j;
91 S[C[j]]++;
92 }
93 }
94 }
95 inline void Link(int r, int c)
96 {
97 D[size] = D[c];
98 U[size] = c;
99 U[D[c]] = size;
100 D[c] = size;
101 if (H[r] < 0)
102 H[r] = L[size] = R[size] = size;
103 else
104 {
105 L[size] = H[r];
106 R[size] = R[H[r]];
107 L[R[H[r]]] = size;
108 R[H[r]] = size;
109 }
110 S[c]++;
111 X[size] = r;
112 C[size++] = c;
113 }
114 bool Dance(int r)
115 {
116 int i, j, temp, c;
117 if (R[0] == 0)
118 {
119 if (!cnt)
120 {
121 for (i = j = 1; i <= r; i++)
122 {
123 if (vis[i])
124 ans[j++] = Q[i];
125 }
126 }
127 cnt++;
128 return cnt > 1;
129 }
130 for (temp = INF,i = R[0]; i; i = R[i])
131 {
132 if (temp > S[i])
133 {
134 temp = S[i];
135 c = i;
136 }
137 }
138 Remove(c);
139 for (i = D[c]; i != c; i = D[i])
140 {
141 vis[X[i]] = true;
142 for (j = R[i]; j != i; j = R[j])
143 Remove(C[j]);
144 if (Dance(r))
145 return true;
146 for (j = L[i]; j != i; j = L[j])
147 Resume(C[j]);
148 vis[X[i]] = false;
149 }
150 Resume(c);
151 return false;
152 }
153 int main()
154 {
155 int c, i, j, k, r, ca = 1;
156 scanf("%d", &c);
157 while (c--)
158 {
159 memset(belong, 0, sizeof(belong));
160 for (i = 0; i < MAXN; i++)
161 {
162 for (j = 0; j < MAXN; j++)
163 scanf("%d", &a[i][j]);
164 }
165 for (i = k = 0; i < MAXN; i++)
166 {
167 for (j = 0; j < MAXN; j++)
168 {
169 if (!belong[i][j])
170 DFS(i, j, ++k);
171 }
172 }
173 Init();
174 for (i = r = 0; i < MAXN; i++)
175 {
176 for (j = 0; j < MAXN; j++)
177 {
178 if (sd[i][j])
179 {
180 k = sd[i][j];
181 H[++r] = -1;
182 Q[r] = k;
183 Link(r, i * 9 + k);
184 Link(r, 81 + j * 9 + k);
185 Link(r, 162 + (belong[i][j] - 1) * 9 + k);
186 Link(r, 243 + i * 9 + j + 1);
187 }
188 else
189 {
190 for (k = 1; k <= MAXN; k++)
191 {
192 H[++r] = -1;
193 Q[r] = k;
194 Link(r, i * 9 + k);
195 Link(r, 81 + j * 9 + k);
196 Link(r, 162 + (belong[i][j] - 1) * 9 + k);
197 Link(r, 243 + i * 9 + j + 1);
198 }
199 }
200 }
201 }
202 cnt = 0;
203 memset(vis, false, sizeof(vis));
204 Dance(r);
205 printf("Case %d:\n", ca++);
206 if (cnt == 0)
207 puts("No solution");
208 else if (cnt > 1)
209 puts("Multiple Solutions");
210 else
211 {
212 for (i = 1; i <= 81; i++)
213 {
214 printf("%d", ans[i]);
215 if (i % 9 == 0)
216 putchar('\n');
217 }
218 }
219 }
220 return 0;
221 }
