/** * author: nok0 * created: 2020.11.06 21:19:56 **/ #ifdef LOCAL #define _GLIBCXX_DEBUG #endif #include using namespace std; #pragma region Macros #define FOR(i, l, r) for(int i = (l); i < (r); ++i) #define REP(i, n) FOR(i, 0, n) #define REPS(i, n) FOR(i, 1, n + 1) #define RFOR(i, l, r) for(int i = (l); i >= (r); --i) #define RREP(i, n) RFOR(i, n - 1, 0) #define RREPS(i, n) RFOR(i, n, 1) #define pb push_back #define eb emplace_back #define SZ(x) ((int)(x).size()) #define all(x) (x).begin(), (x).end() #define rall(x) (x).rbegin(), (x).rend() template using V = vector; template using VV = V>; using ll = long long; using ld = long double; using pii = pair; using pll = pair; #define VEC(type, name, size) \ V name(size); \ INPUT(name) #define VVEC(type, name, h, w) \ VV name(h, V(w)); \ INPUT(name) #define INT(...) \ int __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LL(...) \ ll __VA_ARGS__; \ INPUT(__VA_ARGS__) #define STR(...) \ string __VA_ARGS__; \ INPUT(__VA_ARGS__) #define CHAR(...) \ char __VA_ARGS__; \ INPUT(__VA_ARGS__) #define DOUBLE(...) \ DOUBLE __VA_ARGS__; \ INPUT(__VA_ARGS__) #define LD(...) \ LD __VA_ARGS__; \ INPUT(__VA_ARGS__) void scan(int &a) { cin >> a; } void scan(long long &a) { cin >> a; } void scan(char &a) { cin >> a; } void scan(double &a) { cin >> a; } void scan(long double &a) { cin >> a; } void scan(char a[]) { scanf("%s", a); } void scan(string &a) { cin >> a; } template void scan(V &); template void scan(pair &); template void scan(V &a) { for(auto &i : a) scan(i); } template void scan(pair &p) { scan(p.first); scan(p.second); } template void scan(T &a) { cin >> a; } void INPUT() {} template void INPUT(Head &head, Tail &... tail) { scan(head); INPUT(tail...); } template inline void print(T x) { cout << x << '\n'; } template istream &operator>>(istream &is, pair &p) { is >> p.first >> p.second; return is; } template ostream &operator<<(ostream &os, const pair &p) { os << p.first << " " << p.second; return os; } template istream &operator>>(istream &is, vector &v) { for(T &in : v) is >> in; return is; } template ostream &operator<<(ostream &os, const V &v) { REP(i, SZ(v)) { if(i) os << " "; os << v[i]; } return os; } //debug template void view(const V &v) { cerr << "{ "; for(const auto &e : v) { cerr << e << ", "; } cerr << "\b\b }"; } template void view(const VV &vv) { cerr << "{\n"; for(const auto &v : vv) { cerr << "\t"; view(v); cerr << "\n"; } cerr << "}"; } template void view(const V> &v) { cerr << "{\n"; for(const auto &c : v) cerr << "\t(" << c.first << ", " << c.second << ")\n"; cerr << "}"; } template void view(const map &m) { cerr << "{\n"; for(auto &t : m) cerr << "\t[" << t.first << "] : " << t.second << "\n"; cerr << "}"; } template void view(const pair &p) { cerr << "(" << p.first << ", " << p.second << ")"; } template void view(const set &s) { cerr << "{ "; for(auto &t : s) { view(t); cerr << ", "; } cerr << "\b\b }"; } template void view(T e) { cerr << e; } #ifdef LOCAL void debug_out() {} template void debug_out(Head H, Tail... T) { view(H); cerr << ", "; debug_out(T...); } #define debug(...) \ do { \ cerr << __LINE__ << " [" << #__VA_ARGS__ << "] : ["; \ debug_out(__VA_ARGS__); \ cerr << "\b\b]\n"; \ } while(0) #else #define debug(...) (void(0)) #endif template V press(V &x) { V res = x; sort(all(res)); res.erase(unique(all(res)), res.end()); REP(i, SZ(x)) { x[i] = lower_bound(all(res), x[i]) - res.begin(); } return res; } template inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } template inline bool chmax(T &a, T b) { if(a < b) { a = b; return true; } return false; } inline void Yes(bool b = true) { cout << (b ? "Yes" : "No") << '\n'; } inline void YES(bool b = true) { cout << (b ? "YES" : "NO") << '\n'; } inline void err(bool b = true) { if(b) { cout << -1 << '\n'; exit(0); } } template inline void fin(bool b = true, T e = 0) { if(b) { cout << e << '\n'; exit(0); } } template T divup(T x, T y) { return (x + (y - 1)) / y; } template T pow(T a, long long n, T e = 1) { T ret = e; while(n) { if(n & 1) ret *= a; a *= a; n >>= 1; } return ret; } struct iofast { iofast() { ios::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(15); } } iofast_; const int inf = 1e9; const ll INF = 1e18; #pragma endregion //ModInt template struct ModInt { private: int x; public: ModInt() : x(0) {} ModInt(long long x_) { if((x = x_ % mod + mod) >= mod) x -= mod; } int val() const { return x; } static int get_mod() { return mod; } constexpr ModInt &operator+=(ModInt rhs) { if((x += rhs.x) >= mod) x -= mod; return *this; } constexpr ModInt &operator-=(ModInt rhs) { if((x -= rhs.x) < 0) x += mod; return *this; } constexpr ModInt &operator*=(ModInt rhs) { x = (unsigned long long)x * rhs.x % mod; return *this; } constexpr ModInt &operator/=(ModInt rhs) { x = (unsigned long long)x * rhs.inv().x % mod; return *this; } constexpr ModInt operator-() const noexcept { return -x < 0 ? mod - x : -x; } constexpr ModInt operator+(ModInt rhs) const noexcept { return ModInt(*this) += rhs; } constexpr ModInt operator-(ModInt rhs) const noexcept { return ModInt(*this) -= rhs; } constexpr ModInt operator*(ModInt rhs) const noexcept { return ModInt(*this) *= rhs; } constexpr ModInt operator/(ModInt rhs) const noexcept { return ModInt(*this) /= rhs; } constexpr ModInt &operator++() { *this += 1; return *this; } constexpr ModInt operator++(int) { *this += 1; return *this - 1; } constexpr ModInt &operator--() { *this -= 1; return *this; } constexpr ModInt operator--(int) { *this -= 1; return *this + 1; } bool operator==(ModInt rhs) const { return x == rhs.x; } bool operator!=(ModInt rhs) const { return x != rhs.x; } bool operator<=(ModInt rhs) const { return x <= rhs.x; } bool operator>=(ModInt rhs) const { return x >= rhs.x; } bool operator<(ModInt rhs) const { return x < rhs.x; } bool operator>(ModInt rhs) const { return x > rhs.x; } ModInt inv() { int a = x, b = mod, u = 1, v = 0, t; while(b > 0) { t = a / b; std::swap(a -= t * b, b); std::swap(u -= t * v, v); } return ModInt(u); } ModInt pow(long long n) const { ModInt ret(1), mul(x); while(n > 0) { if(n & 1) ret *= mul; mul *= mul; n >>= 1; } return ret; } ModInt sqrt() const { if(x <= 1) return x; int v = (mod - 1) / 2; if(pow(v) != 1) return -1; int q = mod - 1, m = 0; while(~q & 1) q >>= 1, m++; std::mt19937 mt; ModInt z = mt(); while(z.pow(v) != mod - 1) z = mt(); ModInt c = z.pow(q), t = pow(q), r = pow((q + 1) / 2); for(; m > 1; m--) { ModInt tmp = t.pow(1 << (m - 2)); if(tmp != 1) r = r * c, t = t * c * c; c = c * c; } return std::min(r.x, mod - r.x); } friend std::ostream &operator<<(std::ostream &s, ModInt a) { s << a.x; return s; } friend std::istream &operator>>(std::istream &s, ModInt &a) { s >> a.x; return s; } }; //Modulo Calculation static int MOD = 1e9 + 7; // static int MOD = 998244353; using mint = ModInt; // Binary Indexed Tree (Fenwick Tree) template struct BIT { int n, p; vector d; BIT(int n = 0) : n(n), d(n + 1) { p = 1; while(p < n) p *= 2; } //更新 void add(int i, T x = 1) { for(i++; i <= n; i += i & -i) d[i] += x; } //[0,i)の和 T sum(int i) { T res = 0; for(; i; i -= i & -i) res += d[i]; return res; } //[l,r)の和 T sum(int l, int r) { return sum(r) - sum(l); } //v0+v1+…vx>=mを満たすmin(x)を返す int lower_bound(T w) { if(w <= 0) return 0; T x = 0; for(int i = p; i; i /= 2) { if(i + x <= n && d[i + x] < w) { w -= d[i + x]; x += i; } } return x; } }; int main() { INT(n); VVEC(int, a, n, n); VV dp(1 << (n * 2), V(n, INF)); REP(i, n) { dp[1 << i][i] = 0; } REP(bit, (1 << n * 2)) { REP(to, n) { if(bit >> to & 1 and bit >> (to + n) & 1) continue; REP(from, n) { if(from == to) { if((bit >> to & 1) and __builtin_popcount(bit) == 2 * n - 1) { chmin(dp[(1 << (n * 2)) - 1][to], dp[bit][from]); } else continue; } if(bit >> to & 1) { chmin(dp[bit | (1 << (to + n))][to], dp[bit][from] + a[from][to]); } else chmin(dp[bit | (1 << to)][to], dp[bit][from] + a[from][to]); } } } ll res = INF; REP(i, n) chmin(res, dp[(1 << (2 * n)) - 1][i]); print(res); }