1 #include <iostream>
  2 #include <cstdio>
  3 #include <algorithm>
  4 #include <cstring>
  5 #include <vector>
  6 using namespace std;
  7 typedef long long LL;
  8
  9 const int MAXN = 10;
 10 const int MAXC = 9 * 9 * 4 + 10;
 11 const int MAXR = 9 * 9 * 9 + 10;
 12 const int MAXP = MAXR * 4 + MAXC;
 13
 14 struct DLX {
 15     int sz;
 16     int sum[MAXC];
 17     int row[MAXP], col[MAXP];
 18     int left[MAXP], right[MAXP], up[MAXP], down[MAXP];
 19     int ansd, ans[MAXR], anscnt;
 20
 21     void init(int n) {
 22         for(int i = 0; i <= n; ++i) {
 23             up[i] = down[i] = i;
 24             left[i] = i - 1; right[i] = i + 1;
 25         }
 26         left[0] = n; right[n] = 0;
 27         sz = n + 1;
 28         memset(sum, 0, sizeof(sum));
 29     }
 30
 31     void add_row(int r, vector<int> &func) {
 32         int first = sz;
 33         for(size_t i = 0; i < func.size(); ++i) {
 34             int c = func[i];
 35             left[sz] = sz - 1; right[sz] = sz + 1; up[sz] = up[c]; down[sz] = c;
 36             down[up[c]] = sz; up[c] = sz;
 37             row[sz] = r; col[sz] = c;
 38             ++sum[c], ++sz;
 39         }
 40         left[first] = sz - 1; right[sz - 1] = first;
 41     }
 42
 43     void remove(int c) {
 44         left[right[c]] = left[c];
 45         right[left[c]] = right[c];
 46         for(int i = down[c]; i != c; i = down[i]) {
 47             for(int j = right[i]; j != i; j = right[j])
 48                 up[down[j]] = up[j], down[up[j]] = down[j], --sum[col[j]];
 49         }
 50     }
 51
 52     void restore(int c) {
 53         for(int i = up[c]; i != c; i = up[i]) {
 54             for(int j = left[i]; j != i; j = left[j])
 55                 up[down[j]] = j, down[up[j]] = j, ++sum[col[j]];
 56         }
 57         left[right[c]] = c;
 58         right[left[c]] = c;
 59     }
 60
 61     bool dfs(int d) {
 62         if(!right[0]) {
 63             ansd = d;
 64             return ++anscnt == 2;
 65         }
 66         int c = right[0];
 67         for(int i = right[0]; i != 0; i = right[i]) if(sum[i] < sum[c]) c = i;
 68         remove(c);
 69         for(int i = down[c]; i != c; i = down[i]) {
 70             if(!anscnt) ans[d] = row[i];
 71             for(int j = right[i]; j != i; j = right[j]) remove(col[j]);
 72             if(dfs(d + 1)) return true;
 73             for(int j = left[i]; j != i; j = left[j]) restore(col[j]);
 74         }
 75         restore(c);
 76         return false;
 77     }
 78
 79     int solve(vector<int> &v) {
 80         v.clear();
 81         anscnt = 0;
 82         dfs(0);
 83         if(anscnt == 1) for(int i = 0; i < ansd; ++i) v.push_back(ans[i]);
 84         return anscnt;
 85     }
 86 } solver;
 87
 88 const int SLOT = 0;
 89 const int ROW = 1;
 90 const int COL = 2;
 91 const int SUB = 3;
 92
 93 int fr[] = {-1, 0, 1, 0};
 94 int fc[] = {0, 1, 0, -1};
 95 int fp[] = {16, 32, 64, 128};
 96
 97 int mat[MAXN][MAXN];
 98 int val[MAXN][MAXN], cnt;
 99 int T, n = 9;
100
101 bool in_n(int x) {
102     return 0 <= x && x < n;
103 }
104
105 void dfs(int r, int c, int p) {
106     val[r][c] = p;
107     for(int i = 0; i < 4; ++i) {
108         int nr = r + fr[i], nc = c + fc[i];
109         if(in_n(nr) && in_n(nc) && ((fp[i] & mat[r][c]) == 0) && !val[nr][nc])
110             dfs(nr, nc, p);
111     }
112 }
113
114 void print(int mat[MAXN][MAXN]) {
115     for(int i = 0; i < n; ++i) {
116         for(int j = 0; j < n; ++j) printf("%d", mat[i][j]);
117         puts("");
118     }
119 }
120
121 int encode(int a, int b, int c) {
122     return a * 81 + b * 9 + c + 1;
123 }
124
125 void decode(int code, int &a, int &b, int &c) {
126     --code;
127     c = code % 9; code /= 9;
128     b = code % 9; code /= 9;
129     a = code;
130 }
131
132 int main() {
133     scanf("%d", &T);
134     for(int kase = 1; kase <= T; ++kase) {
135         for(int i = 0; i < n; ++i)
136             for(int j = 0; j < n; ++j) scanf("%d", &mat[i][j]);
137         memset(val, 0, sizeof(val));
138         cnt = 0;
139         for(int i = 0; i < n; ++i)
140             for(int j = 0; j < n; ++j) if(!val[i][j]) dfs(i, j, ++cnt);
141         printf("Case %d:\n", kase);
142         //print(val);
143         solver.init(9 * 9 * 4);
144         for(int r = 0; r < n; ++r)
145             for(int c = 0; c < n; ++c)
146                 for(int i = 0; i < 4; ++i) mat[r][c] &= ~fp[i];
147         //print(mat);
148         for(int r = 0; r < n; ++r) for(int c = 0; c < n; ++c) for(int v = 0; v < n; ++v) {
149             if(!mat[r][c] || mat[r][c] == 1 + v) {
150                 vector<int> func;
151                 func.push_back(encode(SLOT, r, c));
152                 func.push_back(encode(ROW, r, v));
153                 func.push_back(encode(COL, c, v));
154                 func.push_back(encode(SUB, val[r][c] - 1, v));
155                 solver.add_row(encode(r, c, v), func);
156             }
157         }
158         vector<int> ans;
159         int res = solver.solve(ans);
160         if(res == 0) puts("No solution");
161         if(res == 1) {
162             int r, c, v;
163             for(size_t i = 0; i < ans.size(); ++i) {
164                 decode(ans[i], r, c, v);
165                 mat[r][c] = 1 + v;
166             }
167             print(mat);
168         }
169         if(res == 2) puts("Multiple Solutions");
170     }
171 }