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#include <iostream>
#include <iomanip>
#include <string>
#include <vector>
#include <cstring>
#include <cstdint>
#include <cassert>
using namespace std;
struct Sudoku {
int8_t bd[81];
uint16_t poss[81];
int nfull = 0;
Sudoku() {
for (int i = 0; i < 81; i++) {
poss[i] = 0x1ff;
}
}
inline int8_t& operator[](int8_t i) {return bd[i];}
inline const int8_t& operator[](int8_t i) const {return bd[i];}
};
static istream& operator>>(istream &in, Sudoku &su) {
su.nfull = 0;
for (int i = 0; i < 81; i++) {
char c;
in >> c;
if (c == '.') {
su[i] = -1;
} else {
assert('1' <= c && c <= '9');
su[i] = c - '1';
su.nfull++;
}
}
return in;
}
static ostream& operator<<(ostream &os, const Sudoku &su) {
for (int y = 0; y < 9; y++) {
if (y != 0) {
os << endl;
if (y % 3 == 0) os << endl;
}
for (int x = 0; x < 9; x++) {
if (x != 0) {
os << ' ';
if (x % 3 == 0) os << ' ';
}
int8_t v = su[9 * y + x];
if (v == -1) os << '.';
else os << (int)v + 1;
// string s;
// for (int i = 0; i < 9; i++) {
// if (su.poss[9 * y + x] & (1<<i)) s += '1' + i;
// }
// os << '(' << setw(9) << s << ')';
}
}
return os;
}
static bool isValid(const Sudoku &su) {
for (int y = 0; y < 9; y++) {
int i = 9 * y;
uint8_t seen[9];
memset(seen, 0, 9);
for (int x = 0; x < 9; x++, i++) {
int v = su[i];
if (v != -1) {
if (seen[v]) return false;
else seen[v] = 1;
}
}
}
for (int x = 0; x < 9; x++) {
int i = x;
uint8_t seen[9];
memset(seen, 0, 9);
for (int y = 0; y < 9; y++, i += 9) {
int v = su[i];
if (v != -1) {
if (seen[v]) return false;
else seen[v] = 1;
}
}
}
int i = 0;
for (int by = 0; by < 9; by += 3) {
for (int bx = 0; bx < 9; bx += 3) {
uint8_t seen[9];
memset(seen, 0, 9);
int j = i;
for (int y = 0; y < 3; y++) {
for (int x = 0; x < 3; x++) {
int v = su[j];
if (v != -1) {
if (seen[v]) return false;
else seen[v] = 1;
}
j++;
}
j += 6;
}
i += 3;
}
i += 18;
}
return true;
}
vector<Sudoku> solutions;
static void scratchAround(Sudoku &su, int idx, int x, int y) {
uint16_t mask = 0x1ff & ~(1 << su[idx]);
for (int i = 0; i < 9; i++) {
su.poss[9 * y + i] &= mask;
su.poss[9 * i + x] &= mask;
}
int bx = x / 3 * 3, by = y / 3 * 3;
for (int yi = 0; yi < 3; yi++) {
for (int xi = 0; xi < 3; xi++) {
su.poss[9 * (by + yi) + bx + xi] &= mask;
}
}
}
static void scratchAround(Sudoku &su, int idx) {
scratchAround(su, idx, idx % 9, idx / 9);
}
static void scratchAround(Sudoku &su, int x, int y) {
scratchAround(su, 9 * y + x, x, y);
}
static void solveDestructive(Sudoku &su) {
// cerr << "solveDestructive(" << su.nfull << ")" << endl;
for (int y = 0, i = 0; y < 9; y++) {
for (int x = 0; x < 9; x++, i++) {
if (su[i] != -1) continue;
if (__builtin_popcount(su.poss[i]) == 1) {
su[i] = __builtin_ctz(su.poss[i]);
su.nfull++;
scratchAround(su, i);
}
}
}
if (su.nfull == 81) {
if (isValid(su)) {
solutions.push_back(su);
}
return;
}
int mincount = 99, minat = -1;
for (int y = 0, i = 0; y < 9; y++) {
for (int x = 0; x < 9; x++, i++) {
if (su[i] != -1) continue;
int count = __builtin_popcount((uint32_t)su.poss[i]);
if (count < mincount) {
mincount = count;
minat = i;
}
}
}
if (mincount == 1) {
// do a tail call
solveDestructive(su);
return;
}
if (mincount == 0) {
// invalid
return;
}
// cerr << "minat = " << minat << " ";
// cerr << "mincount = " << mincount << endl;
int i = minat;
for (int v = 0; v < 9; v++) {
if ((su.poss[i] & (1 << v)) == 0) continue;
Sudoku su2 = su;
su2[i] = v;
su2.nfull++;
// cerr << "try " << v << endl;
if (!isValid(su2)) {
// cerr << " invalid" << endl;
continue;
}
scratchAround(su2, i);
solveDestructive(su2);
}
}
static void solve(const Sudoku &su) {
Sudoku su2 = su;
solveDestructive(su2);
}
static void cleanPoss(Sudoku &su) {
for (int y = 0; y < 9; y++) {
for (int x = 0; x < 9; x++) {
scratchAround(su, x, y);
}
}
}
int main() {
Sudoku su;
cin >> su;
solutions.clear();
cleanPoss(su);
solve(su);
if (solutions.size() != 1) {
cout << solutions.size() << " solutions found:" << endl;
}
for (const Sudoku &su2 : solutions) {
cout << su2 << endl << endl;
}
}
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