#define _CRT_SECURE_NO_WARNINGS #pragma GCC target("avx") #pragma GCC optimize("O3") #pragma GCC optimize("unroll-loops") #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #include #define rep(i, n) for(int i=0;i<(n);i++) #define REP(i, n) for(int i=1;i<=(n);i++) #define all(V) V.begin(),V.end() typedef long long lint; typedef std::pair P; constexpr int INF = INT_MAX; constexpr lint LINF = LLONG_MAX; constexpr double eps = 1e-9; template class prique :std::priority_queue, std::greater> {}; using namespace std; template> class Vector { using traits = std::allocator_traits; using size_type = unsigned int; class iterator { public: using difference_type = int; using value_type = T; using pointer = T*; using reference = T&; using iterator_category = std::random_access_iterator_tag; private: T* p; public: iterator()noexcept :p(nullptr) {} iterator(Vector* base, difference_type index) noexcept :p(base->e + index) {} iterator(const iterator& i) :p(i.p) {} iterator& operator=(const iterator& i) = default; iterator& operator++() { p++; return *this; } iterator operator++(int) { iterator res = *this; p++; return res; } iterator operator+(const difference_type& x)const { return iterator(*this) += x; } iterator& operator+=(const difference_type& x) { p += x; return *this; } iterator& operator--() { p--; return *this; } iterator operator--(int) { iterator res = *this; p--; return res; } iterator operator-(const difference_type& x)const { return iterator(*this) -= x; } difference_type operator-(const iterator& i)const { return p - i.p; } iterator& operator-=(const difference_type& x) { p -= x; return *this; } reference operator*()const { return *p; } reference operator[](const difference_type& x)const { return *(p + x); } bool operator<(const iterator& i)const { return p < i.p; } bool operator<=(const iterator& i)const { return p <= i.p; } bool operator==(const iterator& i)const { return p == i.p; } bool operator>(const iterator& i)const { return p > i.p; } bool operator>=(const iterator& i)const { return p >= i.p; } bool operator!=(const iterator& i)const { return p != i.p; } }; class const_iterator { public: using difference_type = int; using value_type = T; using pointer = const T*; using reference = const T&; using iterator_category = std::random_access_iterator_tag; private: const T* p; public: const_iterator()noexcept :p(nullptr) {} const_iterator(Vector* base, difference_type index) noexcept :p(base->e + index) {} const_iterator(const iterator& i) :p(i.p) {} const_iterator(const const_iterator& i) :p(i.p) {} const_iterator& operator=(const const_iterator& i) = default; const_iterator& operator++() { p++; return *this; } const_iterator operator++(int) { const_iterator res = *this; p++; return res; } const_iterator operator+(const difference_type& x)const { return const_iterator(*this) += x; } const_iterator& operator+=(const difference_type& x) { p += x; return *this; } const_iterator& operator--() { p--; return *this; } const_iterator operator--(int) { const_iterator res = *this; p--; return res; } const_iterator operator-(const difference_type& x)const { return const_iterator(*this) -= x; } difference_type operator-(const const_iterator& i)const { return p - i.p; } const_iterator& operator-=(const difference_type& x) { p -= x; return *this; } reference operator*()const { return *p; } reference operator[](const difference_type& x)const { return *(p + x); } bool operator<(const const_iterator& i)const { return p < i.p; } bool operator<=(const const_iterator& i)const { return p <= i.p; } bool operator==(const const_iterator& i)const { return p == i.p; } bool operator>(const const_iterator& i)const { return p > i.p; } bool operator>=(const const_iterator& i)const { return p >= i.p; } bool operator!=(const const_iterator& i)const { return p != i.p; } }; using reverse_iterator = std::reverse_iterator; using const_reverse_iterator = std::reverse_iterator; private: T* e; unsigned int length = 0, cap = 1; Alloc alloc; static_assert(std::is_same::value, "The allocator value type is not matched the vector value type."); static_assert(!std::is_const::value, "This library forbids containers of const elements"); public: Vector() :Vector(Alloc()) {} explicit Vector(const Alloc& a) :alloc(a) { e = alloc.allocate(cap); } explicit Vector(size_type n, const Alloc& a = Alloc()) :alloc(a) { while (cap < n)cap *= 2; e = alloc.allocate(cap); rep(i, n)emplace_back(); } explicit Vector(size_type n, const T& value, const Alloc& a = Alloc()) :alloc(a) { while (cap < n)cap *= 2; e = alloc.allocate(cap); rep(i, n)emplace_back(value); } template Vector(InputIter first, InputIter last, const Alloc& a = Alloc()) :alloc(a) { e = alloc.allocate(cap); for (InputIter i = first; i != last; i++) { emplace_back(*i); } } Vector(const Vector& x, const Alloc& a = Alloc()) :alloc(a) { while (cap < x.length)cap *= 2; length = x.length; e = alloc.allocate(cap); rep(i, x.length)traits::construct(alloc, e + i, *(x.e + i)); } Vector(Vector&& x, const Alloc& a = Alloc()) :alloc(a) { cap = x.cap; length = x.length; e = x.e; x.e = nullptr; } ~Vector() { if (e != nullptr) { rep(i, length)traits::destroy(alloc, e + i); alloc.deallocate(e, cap); } } Vector& operator=(const Vector& x) { rep(i, length)traits::destroy(alloc, e + i); alloc.deallocate(e, cap); length = x.length; cap = 1; while (cap < length)cap *= 2; e = alloc.allocate(cap); rep(i, length)traits::construct(alloc, e + i, *(x.e + i)); return *this; } Vector& operator=(Vector&& x) { rep(i, length)traits::destroy(alloc, e + i); alloc.deallocate(e, cap); cap = x.cap; length = x.length; e = x.e; x.e = nullptr; return *this; } private: void extension() { T* e_ = alloc.allocate(cap * 2); rep(i, length)traits::construct(alloc, e_ + i, *(e + i)); rep(i, length)traits::destroy(alloc, e + i); alloc.deallocate(e, cap); e = e_; cap *= 2; } void extension(size_type n) { unsigned int r = 1; while (cap * r < n)r *= 2; if (r == 1)return; T* e_ = alloc.allocate(cap * r); rep(i, length)traits::construct(alloc, e_ + i, *(e + i)); rep(i, length)traits::destroy(alloc, e + i); alloc.deallocate(e, cap); e = e_; cap *= r; } public: template void assign(InputIter first, InputIter last) { unsigned int cnt = 0; for (InputIter i = first; i != last; i++) { if (cnt == cap) { length = std::max(length, cnt); extension(); } traits::construct(alloc, e + cnt, *i); cnt++; } } void assign(size_type n, const T& value) { extension(n); std::fill(e, e + n, value); } template void emplace_back(Args&&... args) { if (length == cap)extension(); traits::construct(alloc, e + length, std::forward(args)...); length++; } void push_back(const T& value) { emplace_back(value); } void push_back(T&& value) { emplace_back(std::move(value)); } void pop_back() { traits::destroy(alloc, e + length); length--; } iterator erase(iterator pos) { const iterator res = pos; iterator t = pos; t++; for (iterator i = pos; t != end(); i++, t++) { *i = std::move(*t); } pop_back(); return res; } iterator erase(iterator first, iterator last) { const iterator res = first; typename iterator::difference_type d = last - first; for (iterator i = first; i + d != end(); i++) { *i = std::move(*(i + d)); } rep(i, d)pop_back(); return res; } void swap(Vector& x) { std::swap(length, x.length); std::swap(cap, x.cap); std::swap(e, x.e); } void clear() { while (length)pop_back(); } size_type size()const { return length; } void resize(size_type n, const T& value = T()) { extension(n); while (n < length)pop_back(); std::fill(e, e + n, value); } size_type capacity()const { return cap; } bool empty()const { return !length; } T& operator[](const unsigned int pos) { return e[pos]; } T* data() { return e; } T& front() { return *e; } T& back() { return *(e + length - 1); } iterator begin() noexcept { return iterator(this, 0); } const_iterator begin()const noexcept { return const_iterator(this, 0); } const_iterator cbegin()const noexcept { return const_iterator(this, 0); } iterator rbegin()noexcept { return reverse_iterator(this, 0); } const_iterator rbegin()const noexcept { return const_reverse_iterator(this, 0); } const_iterator crbegin()const noexcept { return const_reverse_iterator(this, 0); } iterator end() noexcept { return iterator(this, length); } const_iterator end()const noexcept { return const_iterator(this, length); } const_iterator cend()const noexcept { return const_iterator(this, length); } iterator rend()noexcept { return reverse_iterator(this, length); } const_iterator rend()const noexcept { return const_reverse_iterator(this, length); } const_iterator crend()const noexcept { return const_reverse_iterator(this, length); } }; template inline bool chmax(T& lhs, const U& rhs) { if (lhs < rhs) { lhs = rhs; return 1; } return 0; } template inline bool chmin(T& lhs, const U& rhs) { if (lhs > rhs) { lhs = rhs; return 1; } return 0; } inline lint gcd(lint a, lint b) { while (b) { lint c = a; a = b; b = c % b; } return a; } inline lint lcm(lint a, lint b) { return a / gcd(a, b) * b; } bool isprime(lint n) { if (n == 1)return false; for (int i = 2; i * i <= n; i++) { if (n % i == 0)return false; } return true; } lint mypow(lint a, lint b) { if (!b)return 1; if (b & 1)return mypow(a, b - 1) * a; lint memo = mypow(a, b >> 1); return memo * memo; } lint modpow(lint a, lint b, lint m) { if (!b)return 1; if (b & 1)return modpow(a, b - 1, m) * a % m; lint memo = modpow(a, b >> 1, m); return memo * memo % m; } template void printArray(std::vector& vec) { rep(i, vec.size() - 1)std::cout << vec[i] << " "; std::cout << vec.back() << std::endl; } template void printArray(Vector& vec) { rep(i, vec.size() - 1)std::cout << vec[i] << " "; std::cout << vec.back() << std::endl; } template void printArray(T l, T r) { T rprev = r; rprev--; for (T i = l; i != rprev; i++) { std::cout << *i << " "; } std::cout << *rprev << std::endl; } std::string to_string(Vector& vec) { std::string res = "["; rep(i, vec.size() - 1)res += std::to_string(vec[i]) + ", "; res += std::to_string(vec.back()) + "]"; return res; } template class SegTree { protected: int n = 1, rank = 0; vector node; vector lazy; vector lazyflag; vector width; virtual void lazyf(U&, const U&) = 0; virtual void updf(T&, const U&, const unsigned int&) = 0; void eval(int k) { if (!k)return; for (int i = rank; i > 0; i--) { int nk = k >> i; if (lazyflag[nk]) { updf(node[2 * nk], lazy[nk], width[2 * nk]); updf(node[2 * nk + 1], lazy[nk], width[2 * nk + 1]); if (lazyflag[2 * nk])lazyf(lazy[2 * nk], lazy[nk]); else lazy[2 * nk] = lazy[nk]; if (lazyflag[2 * nk + 1])lazyf(lazy[2 * nk + 1], lazy[nk]); else lazy[2 * nk + 1] = lazy[nk]; lazyflag[2 * nk] = lazyflag[2 * nk + 1] = true; lazyflag[nk] = false; } } } public: SegTree(unsigned int m, T init) { while (n < m) { n *= 2; rank++; } node.resize(2 * n); lazy.resize(2 * n); lazyflag.resize(2 * n, false); width.resize(2 * n); for (int i = n; i < 2 * n; i++)node[i] = init; width[1] = n; for (int i = 2; i < 2 * n; i++) { width[i] = width[i >> 1] >> 1; } } SegTree(const vector& initvec) { unsigned int m = initvec.size(); while (n < m) { n *= 2; rank++; } node.resize(2 * n); lazy.resize(2 * n); lazyflag.resize(2 * n, false); width.resize(2 * n); for (int i = n; i < 2 * n; i++) { if (i - n < m)node[i] = initvec[i - n]; } width[1] = n; for (int i = 2; i < 2 * n; i++) { width[i] = width[i >> 1] >> 1; } } virtual void update(int i, U x) { i += n; eval(i); updf(node[i], x, width[i]); if (lazyflag[i])lazyf(lazy[i], x); else { lazyflag[i] = true; lazy[i] = x; } } virtual void update(int l, int r, U x) { l += n; r += n; int nl = l, nr = r; while (!(nl & 1))nl >>= 1; while (!(nr & 1))nr >>= 1; nr--; eval(nl); eval(nr); while (l < r) { if (l & 1) { updf(node[l], x, width[l]); if (lazyflag[l])lazyf(lazy[l], x); else { lazyflag[l] = true; lazy[l] = x; } l++; } if (r & 1) { r--; updf(node[r], x, width[r]); if (lazyflag[r])lazyf(lazy[r], x); else { lazyflag[r] = true; lazy[r] = x; } } l >>= 1; r >>= 1; } } T operator[](const int& x) { eval(x + n); return node[x + n]; } void fill(T x) { std::fill(all(lazyflag), false); std::fill(all(node), x); } void print() { rep(i, n)cout << operator[](i) << " "; cout << endl; } }; class RAQ :public SegTree { void lazyf(lint& a, const lint& b) { a += b; } void updf(lint& a, const lint& b, const unsigned int& width) { a += width * b; } public: RAQ(int size, const lint& def = 0) :SegTree(size, def) {} RAQ(const vector& initvec) :SegTree(initvec) {} }; class RUQ :public SegTree { void lazyf(lint& a, const lint& b) { a = b; } void updf(lint& a, const lint& b, const unsigned int& width) { a = b; } public: RUQ(int size, const lint& def = 0) :SegTree(size, def) {} RUQ(const vector& initvec) :SegTree(initvec) {} }; template class IntervalSegTree :public SegTree { protected: using SegTree::n; using SegTree::rank; using SegTree::node; using SegTree::lazy; using SegTree::lazyflag; using SegTree::width; using SegTree::eval; using SegTree::lazyf; using SegTree::updf; T nodee; virtual T nodef(const T&, const T&)const = 0; public: IntervalSegTree(unsigned int m, T init, T nodee) :SegTree(m, init), nodee(nodee) {} IntervalSegTree(T nodee, const vector& initvec) :SegTree(initvec), nodee(nodee) {} void update(int i, U x) { i += n; eval(i); updf(node[i], x, width[i]); if (lazyflag[i])lazyf(lazy[i], x); else { lazyflag[i] = true; lazy[i] = x; } while (i /= 2)node[i] = nodef(node[2 * i], node[2 * i + 1]); } void update(int l, int r, U x) { l += n; r += n; int nl = l, nr = r; while (!(nl & 1))nl >>= 1; while (!(nr & 1))nr >>= 1; nr--; eval(nl); eval(nr); while (l < r) { if (l & 1) { updf(node[l], x, width[l]); if (lazyflag[l])lazyf(lazy[l], x); else { lazyflag[l] = true; lazy[l] = x; } l++; } if (r & 1) { r--; updf(node[r], x, width[r]); if (lazyflag[r])lazyf(lazy[r], x); else { lazyflag[r] = true; lazy[r] = x; } } l >>= 1; r >>= 1; } while (nl >>= 1)node[nl] = nodef(node[2 * nl], node[2 * nl + 1]); while (nr >>= 1)node[nr] = nodef(node[2 * nr], node[2 * nr + 1]); } T query(int l, int r) { l += n; r += n; eval(l); eval(r - 1); int ls = nodee, rs = nodee; while (l < r) { if (l & 1) { ls = nodef(ls, node[l]); l++; } if (r & 1) { r--; rs = nodef(node[r], rs); } l >>= 1; r >>= 1; } return nodef(ls, rs); } T queryForAll() { return node[1]; } void print() { rep(i, n)cout << SegTree::query(i) << " "; cout << endl; } }; class RAQRSQ :public IntervalSegTree { lint nodef(const lint& a, const lint& b)const { return a + b; } void lazyf(lint& a, const lint& b) { a += b; } void updf(lint& a, const lint& b, const unsigned int& width) { a += width * b; } public: RAQRSQ(int size, const lint& def = 0) :IntervalSegTree(size, def, 0) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } RAQRSQ(const vector& initvec) :IntervalSegTree((lint)0, initvec) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } }; class RAQRMiQ :public IntervalSegTree { lint nodef(const lint& a, const lint& b)const { return min(a, b); } void lazyf(lint& a, const lint& b) { a += b; } void updf(lint& a, const lint& b, const unsigned int& width) { a += b; } public: RAQRMiQ(int size, const lint& def = 0) :IntervalSegTree(size, def, LINF) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } RAQRMiQ(const vector& initvec) :IntervalSegTree(LINF, initvec) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } }; class RAQRMaQ :public IntervalSegTree { lint nodef(const lint& a, const lint& b)const { return max(a, b); } void lazyf(lint& a, const lint& b) { a += b; } void updf(lint& a, const lint& b, const unsigned int& width) { a += b; } public: RAQRMaQ(unsigned int size, const lint& def = 0) :IntervalSegTree(size, def, -LINF) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } RAQRMaQ(const vector& initvec) :IntervalSegTree(-LINF, initvec) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } }; class RUQRSQ :public IntervalSegTree { lint nodef(const lint& a, const lint& b)const { return a + b; } void lazyf(lint& a, const lint& b) { a = b; } void updf(lint& a, const lint& b, const unsigned int& width) { a = width * b; } public: RUQRSQ(int size, const int& def = 0) :IntervalSegTree(size, def, 0) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } RUQRSQ(const vector& initvec) :IntervalSegTree((lint)0, initvec) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } }; class RUQRMiQ :public IntervalSegTree { lint nodef(const int& a, const int& b)const { return min(a, b); } void lazyf(int& a, const int& b) { a = b; } void updf(int& a, const int& b, const unsigned int& width) { a = b; } public: RUQRMiQ(int size, const lint& def = 0) :IntervalSegTree(size, def, LINF) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } RUQRMiQ(const vector& initvec) :IntervalSegTree(LINF, initvec) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } }; class RUQRMaQ :public IntervalSegTree { lint nodef(const lint& a, const lint& b)const { return max(a, b); } void lazyf(lint& a, const lint& b) { a = b; } void updf(lint& a, const lint& b, const unsigned int& width) { a = b; } public: RUQRMaQ(int size, const lint& def = 0) :IntervalSegTree(size, def, -LINF) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } RUQRMaQ(const vector& initvec) :IntervalSegTree(-LINF, initvec) { for (int i = n - 1; i > 0; i--)node[i] = nodef(node[2 * i], node[2 * i + 1]); } }; int n, a[1010][1010], b[2][1010]; Vector

home[1010]; int main() { std::cin >> n; rep(i, n) { rep(j, n) { std::cin >> a[i][j]; home[a[i][j]].emplace_back(i, j); } } lint ans = 0; RAQRSQ st1(n), st2(n); REP(i, n) { st1.fill(0); st2.fill(0); for (P j : home[i]) { if (j.first + j.second + 1 < n)st1.update(j.first + j.second + 1, n, 1); if (0 <= j.first - j.second - 1)st2.update(0, j.first - j.second, 1); ans += j.second; } rep(j, n - 1)st1.update(j + 1, j + 2, st1[j]); for (int j = n - 1; j > 0; j--)st2.update(j - 1, j, st2[j]); int cnt = INF; rep(j, n)chmin(cnt, st1[j] + st2[j]); ans += cnt; } std::cout << ans << std::endl; return 0; }