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#include <bits/stdc++.h>
using namespace std;
class DLX {
protected:
struct Node {
size_t l, r, u, d, row, col;
constexpr Node(size_t l = 0,
size_t r = 0,
size_t u = 0,
size_t d = 0,
size_t row = 0,
size_t col = 0)
: l(l), r(r), u(u), d(d), row(row), col(col) {}
friend std::ostream &operator<<(std::ostream &os, Node const &data) {
return os << data.l << ' ' << data.r << ' ' << data.u << ' ' << data.d
<< ' ' << data.row << ' ' << data.col;
}
};
std::vector<Node> data;
std::vector<size_t> cnt_col;
bool multians;
#define l_(x) data[x].l
#define r_(x) data[x].r
#define u_(x) data[x].u
#define d_(x) data[x].d
#define row_(x) data[x].row
#define col_(x) data[x].col
#define for_(i, start, dir) \
for (size_t start__ = (start), i = dir##_(start__); i != start__; \
i = dir##_(i))
void remove_(size_t col) {
r_(l_(col)) = r_(col);
l_(r_(col)) = l_(col);
for_(i, col, d)
for_(j, i, r) {
u_(d_(j)) = u_(j);
d_(u_(j)) = d_(j);
--cnt_col[col_(j)];
}
}
void resume_(size_t col) {
r_(l_(col)) = l_(r_(col)) = col;
for_(i, col, u)
for_(j, i, r) {
u_(d_(j)) = d_(u_(j)) = j;
++cnt_col[col_(j)];
}
}
bool dance_(std::vector<size_t> &ans_,
std::function<void(std::vector<size_t> const &)> const &func_) {
size_t now = r_(0);
if (now == 0) return func_(ans_), true;
for_(i, 0, r)
if (cnt_col[i] < cnt_col[now]) now = i;
remove_(now);
bool ret = false;
for_(i, now, d) {
ans_.push_back(row_(i));
for_(j, i, r) remove_(col_(j));
ret |= dance_(ans_, func_);
for_(j, i, l) resume_(col_(j));
if (!multians && ret) return true;
ans_.pop_back();
}
resume_(now);
return ret;
}
void ins_row_(size_t row, const std::vector<size_t> &cols) {
assert(row > 0);
size_t sz = data.size();
for (size_t i = 0; i < cols.size(); ++i) {
data.emplace_back(
sz + i - 1, sz + i + 1, u_(cols[i]), cols[i], row, cols[i]);
u_(cols[i]) = d_(u_(cols[i])) = sz + i;
++cnt_col[cols[i]];
if (d_(cols[i]) == cols[i]) d_(cols[i]) = sz + i;
}
r_(l_(sz) = data.size() - 1) = sz;
}
public:
explicit DLX(size_t width, bool multi_ans = false)
: data(), cnt_col(), multians(multi_ans) {
reset(width);
}
explicit DLX(std::vector<std::vector<bool>> const &grid,
bool multi_ans = false)
: data(), cnt_col(), multians(multi_ans) {
reset_grid(grid);
}
friend std::ostream &operator<<(std::ostream &os, DLX const &dlx) {
os << dlx.data[0].l << ' ' << dlx.cnt_col.size() << ' ' << dlx.data.size()
<< '\n';
for (size_t i = 1; i < dlx.cnt_col.size(); ++i)
os << dlx.cnt_col[i] << " \n"[i == dlx.cnt_col.size() - 1];
for (size_t i = 0; i < dlx.data.size(); ++i)
os << i << ": " << dlx.data[i] << '\n';
return os;
}
void reset(size_t width) {
assert(width > 0);
data.clear();
cnt_col.resize(width + 1, 0);
for (size_t i = 0; i <= width; ++i)
data.emplace_back(i - 1, i + 1, i, i, 0, i);
r_(l_(0) = width) = 0;
}
void reset_grid(std::vector<std::vector<bool>> const &grid) {
size_t col = grid[0].size();
for (size_t i = 1; i < grid.size(); ++i)
col = std::max(col, grid[i].size());
reset(col);
std::vector<size_t> _;
for (size_t i = 0; i < grid.size(); ++i) {
_.clear();
for (size_t j = 0; j < grid[i].size(); ++j)
if (grid[i][j]) _.push_back(j + 1);
if (!_.empty()) ins_row_(i + 1, _);
}
}
std::pair<bool, std::vector<size_t>>
dance(std::function<void(std::vector<size_t> const &)> func =
[](auto const &) {}) {
std::vector<size_t> ans;
return {dance_(ans, func), ans};
}
#undef l_
#undef r_
#undef u_
#undef d_
#undef row_
#undef col_
#undef for_
};
int sdk[9][9];
template <class Ch,
class Tr,
class Ct,
std::enable_if_t<std::is_same_v<decltype(std::declval<Ct>().begin()),
typename Ct::iterator> &&
std::is_same_v<decltype(std::declval<Ct>().end()),
typename Ct::iterator>> * = nullptr>
std::basic_ostream<Ch, Tr> &operator<<(std::basic_ostream<Ch, Tr> &os,
const Ct &x) {
if (x.begin() == x.end()) return os;
for (auto it = x.begin(); it != x.end() - 1; ++it) os << *it << ' ';
os << x.back();
return os;
}
const int score[9][9] = {{6, 6, 6, 6, 6, 6, 6, 6, 6},
{6, 7, 7, 7, 7, 7, 7, 7, 6},
{6, 7, 8, 8, 8, 8, 8, 7, 6},
{6, 7, 8, 9, 9, 9, 8, 7, 6},
{6, 7, 8, 9, 10, 9, 8, 7, 6},
{6, 7, 8, 9, 9, 9, 8, 7, 6},
{6, 7, 8, 8, 8, 8, 8, 7, 6},
{6, 7, 7, 7, 7, 7, 7, 7, 6},
{6, 6, 6, 6, 6, 6, 6, 6, 6}};
int main() {
ios::sync_with_stdio(false);
cin.tie(nullptr);
cout.tie(nullptr);
for (int i = 0; i < 9; ++i)
for (int j = 0; j < 9; ++j) cin >> sdk[i][j];
vector<vector<bool>> maps(729, vector<bool>(324));
for (int i = 0; i < 9; ++i)
for (int j = 0; j < 9; ++j) {
for (int k = 1; k <= 9; ++k) {
if (sdk[i][j] && sdk[i][j] != k) continue;
auto _ = (k - 1) * 81 + i * 9 + j;
maps[_][i * 9 + j] = maps[_][i * 9 + k + 80] =
maps[_][j * 9 + k + 161] =
maps[_][(i / 3 * 3 + j / 3) * 9 + k + 242] = true;
}
}
int max_score = -1;
auto func = [&](const vector<size_t> &res) {
for (auto &&_ : res) {
auto k = (_ - 1) / 81 + 1, i = (_ - 1) % 81 / 9, j = (_ - 1) % 9;
sdk[i][j] = k;
}
int now_score = 0;
for (int i = 0; i < 9; ++i)
for (int j = 0; j < 9; ++j) now_score += score[i][j] * sdk[i][j];
max_score = max(max_score, now_score);
};
auto &&[flag, res] = DLX(maps, true).dance(func);
cout << max_score;
return 0;
}
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