結果
| 問題 | No.1169 Row and Column and Diagonal |
| ユーザー |
 kotamanegi
|
| 提出日時 | 2020-08-14 21:26:02 |
| 言語 | C++17(clang) (17.0.6 + boost 1.83.0) |
| 結果 |
AC
|
| 実行時間 | 79 ms / 2,000 ms |
| コード長 | 29,951 bytes |
| コンパイル時間 | 2,898 ms |
| コンパイル使用メモリ | 208,404 KB |
| 実行使用メモリ | 77,568 KB |
| 最終ジャッジ日時 | 2024-10-15 14:40:00 |
| 合計ジャッジ時間 | 4,931 ms |
|
ジャッジサーバーID （参考情報） |
judge4 / judge3 |
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テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | AC | 58 ms
73,856 KB |
| testcase_01 | AC | 58 ms
73,856 KB |
| testcase_02 | AC | 58 ms
73,728 KB |
| testcase_03 | AC | 59 ms
73,856 KB |
| testcase_04 | AC | 60 ms
73,728 KB |
| testcase_05 | AC | 59 ms
73,856 KB |
| testcase_06 | AC | 60 ms
74,368 KB |
| testcase_07 | AC | 63 ms
75,008 KB |
| testcase_08 | AC | 66 ms
75,392 KB |
| testcase_09 | AC | 71 ms
75,776 KB |
| testcase_10 | AC | 77 ms
77,184 KB |
| testcase_11 | AC | 78 ms
77,568 KB |
| testcase_12 | AC | 79 ms
77,568 KB |
| testcase_13 | AC | 78 ms
77,568 KB |
| testcase_14 | AC | 78 ms
77,568 KB |
コンパイルメッセージ
main.cpp:4:18: warning: '#pragma comment linker' ignored [-Wignored-pragmas]
4 | #pragma comment (linker, "/STACK:526000000")
| ^
main.cpp:987:9: warning: 'int' macro redefined [-Wmacro-redefined]
987 | #define int unsigned long long
| ^
main.cpp:874:9: note: previous definition is here
874 | #define int ll
| ^
2 warnings generated.
ソースコード
#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#pragma comment (linker, "/STACK:526000000")
#include "bits/stdc++.h"
#define int ll
using namespace std;
typedef string::const_iterator State;
#define eps 1e-8L
#define MAX_MOD 1000000007LL
#define GYAKU 500000004LL
#define MOD 998244353LL
#define pb push_back
#define mp make_pair
typedef long long ll;
typedef long double ld;
#define REP(a,b) for(long long (a) = 0;(a) < (b);++(a))
#define ALL(x) (x).begin(),(x).end()
template <std::uint_fast64_t mod>
class modint {
public:
using u64 = std::uint_fast64_t;
u64 value = 0;
modint() :value(0LL) {
}
modint(ll a) : value(a% mod) {
}
constexpr modint operator+(const modint rhs) const {
return modint(*this) += rhs;
}
constexpr modint operator-(const modint rhs) const {
return modint(*this) -= rhs;
}
constexpr modint operator*(const modint rhs) const {
return modint(*this) *= rhs;
}
constexpr modint operator/(const modint rhs) const {
return modint(*this) /= rhs;
}
constexpr modint& operator+=(const modint rhs) {
value += rhs.value;
if (value >= mod) {
value -= mod;
}
return *this;
}
constexpr modint& operator-=(const modint rhs) {
if (value < rhs.value) {
value += mod;
}
value -= rhs.value;
value += mod;
value %= mod;
return *this;
}
constexpr modint& operator*=(const modint rhs) {
value = (value * rhs.value) % mod;
return *this;
}
constexpr modint& operator/=(modint rhs) {
ll rem = mod - 2;
while (rem) {
if (rem % 2) {
*this *= rhs;
}
rhs *= rhs;
rem /= 2LL;
}
return *this;
}
bool operator <(modint rhs) const {
return value < rhs.value;
}
friend ostream& operator<<(ostream& os, modint& p) {
os << p.value;
return (os);
}
};
unsigned long xor128() {
static unsigned long x = 123456789, y = 362436069, z = 521288629, w = 88675123;
unsigned long t = (x ^ (x << 11));
x = y; y = z; z = w;
return (w = (w ^ (w >> 19)) ^ (t ^ (t >> 8)));
}
//in ICPC do not use library below!
typedef complex<long double> Point;
typedef pair<complex<long double>, complex<long double>> Line;
typedef struct Circle {
complex<long double> center;
long double r;
}Circle;
long double dot(Point a, Point b) {
return (a.real() * b.real() + a.imag() * b.imag());
}
long double cross(Point a, Point b) {
return (a.real() * b.imag() - a.imag() * b.real());
}
long double Dist_Line_Point(Line a, Point b) {
if (dot(a.second - a.first, b - a.first) < eps) return abs(b - a.first);
if (dot(a.first - a.second, b - a.second) < eps) return abs(b - a.second);
return abs(cross(a.second - a.first, b - a.first)) / abs(a.second - a.first);
}
int is_intersected_ls(Line a, Line b) {
return (cross(a.second - a.first, b.first - a.first) * cross(a.second - a.first, b.second - a.first) < eps) &&
(cross(b.second - b.first, a.first - b.first) * cross(b.second - b.first, a.second - b.first) < eps);
}
Point intersection_l(Line a, Line b) {
Point da = a.second - a.first;
Point db = b.second - b.first;
return a.first + da * cross(db, b.first - a.first) / cross(db, da);
}
long double Dist_Line_Line(Line a, Line b) {
if (is_intersected_ls(a, b) == 1) {
return 0;
}
return min({ Dist_Line_Point(a,b.first), Dist_Line_Point(a,b.second),Dist_Line_Point(b,a.first),Dist_Line_Point(b,a.second) });
}
pair<Point, Point> intersection_Circle_Circle(Circle a, Circle b) {
long double dist = abs(a.center - b.center);
assert(dist <= eps + a.r + b.r);
assert(dist + eps >= abs(a.r - b.r));
Point target = b.center - a.center;
long double pointer = target.real() * target.real() + target.imag() * target.imag();
long double aa = pointer + a.r * a.r - b.r * b.r;
aa /= 2.0L;
Point l{ (aa * target.real() + target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
(aa * target.imag() - target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
Point r{ (aa * target.real() - target.imag() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer,
(aa * target.imag() + target.real() * sqrt(pointer * a.r * a.r - aa * aa)) / pointer };
r = r + a.center;
l = l + a.center;
return mp(l, r);
}
//end of geometry
ll gcd(ll a, ll b) {
if (b == 0) return a;
return gcd(b, a % b);
}
template<typename A>
A pows(A val, ll b) {
assert(b >= 1);
A ans = val;
b--;
while (b) {
if (b % 2) {
ans *= val;
}
val *= val;
b /= 2LL;
}
return ans;
}
template<typename A>
class Compressor {
public:
bool is_zipped = false;
map<A, ll> zipper;
map<ll, A> unzipper;
queue<A> fetcher;
Compressor() {
is_zipped = false;
zipper.clear();
unzipper.clear();
}
void add(A now) {
assert(is_zipped == false);
zipper[now] = 1;
fetcher.push(now);
}
void exec() {
assert(is_zipped == false);
int cnt = 0;
for (auto i = zipper.begin(); i != zipper.end(); ++i) {
i->second = cnt;
unzipper[cnt] = i->first;
cnt++;
}
is_zipped = true;
}
ll fetch() {
assert(is_zipped == true);
A hoge = fetcher.front();
fetcher.pop();
return zipper[hoge];
}
ll zip(A now) {
assert(is_zipped == true);
assert(zipper.find(now) != zipper.end());
return zipper[now];
}
A unzip(ll a) {
assert(is_zipped == true);
assert(a < unzipper.size());
return unzipper[a];
}
ll next(A now) {
auto x = zipper.upper_bound(now);
if (x == zipper.end()) return zipper.size();
return (ll)((*x).second);
}
ll back(A now) {
auto x = zipper.lower_bound(now);
if (x == zipper.begin()) return -1;
x--;
return (ll)((*x).second);
}
};
template<typename A>
class Matrix {
public:
vector<vector<A>> data;
Matrix(vector<vector<A>> a) :data(a) {
}
Matrix operator + (const Matrix obj) {
vector<vector<A>> ans;
assert(obj.data.size() == this->data.size());
assert(obj.data[0].size() == this->data[0].size());
REP(i, obj.data.size()) {
ans.push_back(vector<A>());
REP(q, obj.data[i].size()) {
A hoge = obj.data[i][q] + (this->data[i][q]);
ans.back().push_back(hoge);
}
}
return Matrix(ans);
}
Matrix operator - (const Matrix obj) {
vector<vector<A>> ans;
assert(obj.data.size() == this->data.size());
assert(obj.data[0].size() == this->data[0].size());
REP(i, obj.data.size()) {
ans.push_back(vector<A>());
REP(q, obj.data[i].size()) {
A hoge = this->data[i][q] - obj.data[i][q];
ans.back().push_back(hoge);
}
}
return Matrix(ans);
}
Matrix operator * (const Matrix obj) {
vector<vector<A>> ans;
assert(obj.data.size() == this->data[0].size());
REP(i, this -> data.size()) {
ans.push_back(vector<A>());
REP(q, obj.data[0].size()) {
A hoge = ((this->data[i][0]) * (obj.data[0][q]));
for (int t = 1; t < obj.data.size(); ++t) {
hoge += ((this->data[i][t]) * obj.data[t][q]);
}
ans.back().push_back(hoge);
}
}
return Matrix(ans);
}
Matrix& operator *= (const Matrix obj) {
*this = (*this * obj);
return *this;
}
Matrix& operator += (const Matrix obj) {
*this = (*this + obj);
return *this;
}
Matrix& operator -= (const Matrix obj) {
*this = (*this - obj);
return *this;
}
};
struct Fraction {
ll a;
ll b;
Fraction() :a(0LL), b(1LL) {
}
Fraction(ll c, ll d) {
int hoge = gcd(llabs(c), llabs(d));
if (hoge != 0) {
c /= hoge;
d /= hoge;
if (d < 0 or (d == 0 and c < 0)) {
d *= -1;
c *= -1;
}
}
a = c;
b = d;
}
bool operator <(Fraction rhs) const {
if (a < 0 and rhs.a > 0) return 1;
if (a > 0 and rhs.a < 0) return 0;
return a * rhs.b < rhs.a* b;
}
bool operator ==(Fraction rhs) const {
return a == rhs.a and b == rhs.b;
}
};
class Dice {
public:
vector<ll> vertexs;
//Up: 0,Left: 1,Center: 2,Right: 3,Adj: 4, Down: 5
Dice(vector<ll> init) :vertexs(init) {
}
//Look from Center
void RtoL() {
for (int q = 1; q < 4; ++q) {
swap(vertexs[q], vertexs[q + 1]);
}
}
void LtoR() {
for (int q = 3; q >= 1; --q) {
swap(vertexs[q], vertexs[q + 1]);
}
}
void UtoD() {
swap(vertexs[5], vertexs[4]);
swap(vertexs[2], vertexs[5]);
swap(vertexs[0], vertexs[2]);
}
void DtoU() {
swap(vertexs[0], vertexs[2]);
swap(vertexs[2], vertexs[5]);
swap(vertexs[5], vertexs[4]);
}
bool ReachAble(Dice now) {
set<Dice> hoge;
queue<Dice> next;
next.push(now);
hoge.insert(now);
while (next.empty() == false) {
Dice seeing = next.front();
next.pop();
if (seeing == *this) return true;
seeing.RtoL();
if (hoge.count(seeing) == 0) {
hoge.insert(seeing);
next.push(seeing);
}
seeing.LtoR();
seeing.LtoR();
if (hoge.count(seeing) == 0) {
hoge.insert(seeing);
next.push(seeing);
}
seeing.RtoL();
seeing.UtoD();
if (hoge.count(seeing) == 0) {
hoge.insert(seeing);
next.push(seeing);
}
seeing.DtoU();
seeing.DtoU();
if (hoge.count(seeing) == 0) {
hoge.insert(seeing);
next.push(seeing);
}
}
return false;
}
bool operator ==(const Dice& a) {
for (int q = 0; q < 6; ++q) {
if (a.vertexs[q] != (*this).vertexs[q]) {
return false;
}
}
return true;
}
bool operator <(const Dice& a) const {
return (*this).vertexs < a.vertexs;
}
};
pair<Dice, Dice> TwoDimDice(int center, int up) {
int target = 1;
while (true) {
if (center != target && 7 - center != target && up != target && 7 - up != target) {
break;
}
target++;
}
return mp(Dice(vector<ll>{up, target, center, 7 - target, 7 - center, 7 - up}), Dice(vector<ll>{up, 7 - target, center, target, 7 - center, 7 - up}));
}
tuple<Dice, Dice, Dice, Dice> OneDimDice(int center) {
int bo = min(center, 7 - center);
pair<int, int> goa;
if (bo == 1) {
goa = mp(2, 3);
}
else if (bo == 2) {
goa = mp(1, 3);
}
else if (bo == 3) {
goa = mp(1, 2);
}
tuple<Dice, Dice, Dice, Dice> now = make_tuple(Dice(vector<ll>{goa.first, goa.second, center, 7 - goa.second, 7 - center, 7 - goa.first}),
Dice(vector<ll>{goa.first, 7 - goa.second, center, goa.second, 7 - center, 7 - goa.first}),
Dice(vector<ll>{7 - goa.first, goa.second, center, 7 - goa.second, 7 - center, goa.first}),
Dice(vector<ll>{7 - goa.first, 7 - goa.second, center, goa.second, 7 - center, goa.first}));
return now;
}
template<typename A, typename B>
class Dijkstra {
public:
vector<vector<pair<int, A>>> vertexs;
B Cost_Function;
Dijkstra(int n, B cost) : Cost_Function(cost) {
vertexs = vector<vector<pair<int, A>>>(n, vector<pair<int, A>>{});
}
~Dijkstra() {
vertexs.clear();
}
void add_edge(int a, int b, A c) {
vertexs[a].push_back(mp(b, c));
}
vector<ll> build_result(int StartPoint) {
vector<ll> dist(vertexs.size(), 2e18);
dist[StartPoint] = 0;
priority_queue<pair<ll, int>, vector<pair<ll, int>>, greater<pair<ll, int>>> next;
next.push(make_pair(0, StartPoint));
while (next.empty() == false) {
pair<ll, int> now = next.top();
next.pop();
if (dist[now.second] != now.first) continue;
for (auto x : vertexs[now.second]) {
ll now_cost = now.first + Cost_Function(x.second);
if (dist[x.first] > now_cost) {
dist[x.first] = now_cost;
next.push(mp(now_cost, x.first));
}
}
}
return dist;
}
};
class Dinic {
public:
struct edge {
int to;
int cap;
int rev;
};
vector<vector<edge>> Graph;
vector<int> level;
vector<int> itr;
Dinic(int n) {
Graph = vector<vector<edge>>(n, vector<edge>());
}
void add_edge(int a, int b, int cap) {
Graph[a].push_back(edge{ b, cap ,(int)Graph[b].size() });
Graph[b].push_back(edge{ a,0,(int)Graph[a].size() - 1 });
}
void bfs(int s) {
level = vector<int>(Graph.size(), -1);
level[s] = 0;
queue<int> next;
next.push(s);
while (next.empty() == false) {
int now = next.front();
next.pop();
for (auto x : Graph[now]) {
if (x.cap == 0) continue;
if (level[x.to] == -1) {
level[x.to] = level[now] + 1;
next.push(x.to);
}
}
}
}
int dfs(int now, int goal, int val) {
if (goal == now) return val;
for (int& i = itr[now]; i < (int)Graph[now].size(); ++i) {
edge& target = Graph[now][i];
if (target.cap > 0 && level[now] < level[target.to]) {
int d = dfs(target.to, goal, min(val, target.cap));
if (d > 0) {
target.cap -= d;
Graph[target.to][target.rev].cap += d;
return d;
}
}
}
return 0;
}
int run(int s, int t) {
int ans = 0;
int f = 0;
while (bfs(s), level[t] >= 0) {
itr = vector<int>(Graph.size(), 0);
while ((f = dfs(s, t, 1e9)) > 0) {
ans += f;
}
}
return ans;
}
};
class HLDecomposition {
public:
vector<vector<int>> vertexs;
vector<int> depth;
vector<int> backs;
vector<int> connections;
vector<int> zip, unzip;
HLDecomposition(int n) {
vertexs = vector<vector<int>>(n, vector<int>());
depth = vector<int>(n);
zip = vector<int>(n);
unzip = zip;
}
void add_edge(int a, int b) {
vertexs[a].push_back(b);
vertexs[b].push_back(a);
}
int depth_dfs(int now, int back) {
depth[now] = 0;
for (auto x : vertexs[now]) {
if (x == back) continue;
depth[now] = max(depth[now], 1 + depth_dfs(x, now));
}
return depth[now];
}
void dfs(int now, int backing) {
zip[now] = backs.size();
unzip[backs.size()] = now;
backs.push_back(backing);
int now_max = -1;
int itr = -1;
for (auto x : vertexs[now]) {
if (depth[x] > depth[now]) continue;
if (now_max < depth[x]) {
now_max = depth[x];
itr = x;
}
}
if (itr == -1) return;
connections.push_back(connections.back());
dfs(itr, backing);
for (auto x : vertexs[now]) {
if (depth[x] > depth[now]) continue;
if (x == itr) continue;
connections.push_back(zip[now]);
dfs(x, backs.size());
}
return;
}
void build() {
depth_dfs(0, -1);
connections.push_back(-1);
dfs(0, -1);
}
vector<pair<int, int>> query(int a, int b) {
a = zip[a];
b = zip[b];
vector<pair<int, int>> ans;
while (backs[a] != backs[b]) {
if (a < b) swap(a, b);
ans.push_back(mp(backs[a], a + 1));
a = connections[a];
}
if (a > b) swap(a, b);
ans.push_back(mp(a, b + 1));
return ans;
}
int lca(int a, int b) {
a = zip[a];
b = zip[b];
while (backs[a] != backs[b]) {
if (a < b) swap(a, b);
a = connections[a];
}
return unzip[min(a, b)];
}
};
//by ei1333
//https://ei1333.github.io/luzhiled/snippets/structure/segment-tree.html
template< typename Monoid >
struct SegmentTree {
using F = function< Monoid(Monoid, Monoid) >;
int sz;
vector< Monoid > seg;
const F f;
const Monoid M1;
SegmentTree(int n, const F f, const Monoid& M1) : f(f), M1(M1) {
sz = 1;
while (sz < n) sz <<= 1;
seg.assign(2 * sz + 1, M1);
}
void set(int k, const Monoid& x) {
seg[k + sz] = x;
}
void build() {
for (int k = sz - 1; k > 0; k--) {
seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
}
}
void update(int k, const Monoid& x) {
k += sz;
seg[k] = x;
while (k >>= 1) {
seg[k] = f(seg[2 * k + 0], seg[2 * k + 1]);
}
}
Monoid query(int a, int b) {
Monoid L = M1, R = M1;
for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
if (a & 1) L = f(L, seg[a++]);
if (b & 1) R = f(seg[--b], R);
}
return f(L, R);
}
Monoid operator[](const int& k) const {
return seg[k + sz];
}
template< typename C >
int find_subtree(int a, const C& check, Monoid& M, bool type) {
while (a < sz) {
Monoid nxt = type ? f(seg[2 * a + type], M) : f(M, seg[2 * a + type]);
if (check(nxt)) a = 2 * a + type;
else M = nxt, a = 2 * a + 1 - type;
}
return a - sz;
}
template< typename C >
int find_first(int a, const C& check) {
Monoid L = M1;
if (a <= 0) {
if (check(f(L, seg[1]))) return find_subtree(1, check, L, false);
return -1;
}
int b = sz;
for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
if (a & 1) {
Monoid nxt = f(L, seg[a]);
if (check(nxt)) return find_subtree(a, check, L, false);
L = nxt;
++a;
}
}
return -1;
}
template< typename C >
int find_last(int b, const C& check) {
Monoid R = M1;
if (b >= sz) {
if (check(f(seg[1], R))) return find_subtree(1, check, R, true);
return -1;
}
int a = sz;
for (b += sz; a < b; a >>= 1, b >>= 1) {
if (b & 1) {
Monoid nxt = f(seg[--b], R);
if (check(nxt)) return find_subtree(b, check, R, true);
R = nxt;
}
}
return -1;
}
};
template< typename Monoid, typename OperatorMonoid = Monoid >
struct LazySegmentTree {
using F = function< Monoid(Monoid, Monoid) >;
using G = function< Monoid(Monoid, OperatorMonoid) >;
using H = function< OperatorMonoid(OperatorMonoid, OperatorMonoid) >;
int sz, height;
vector< Monoid > data;
vector< OperatorMonoid > lazy;
const F f;
const G g;
const H h;
const Monoid M1;
const OperatorMonoid OM0;
LazySegmentTree(int n, const F f, const G g, const H h,
const Monoid& M1, const OperatorMonoid OM0)
: f(f), g(g), h(h), M1(M1), OM0(OM0) {
sz = 1;
height = 0;
while (sz < n) sz <<= 1, height++;
data.assign(2 * sz, M1);
lazy.assign(2 * sz, OM0);
}
void set(int k, const Monoid& x) {
data[k + sz] = x;
}
void build() {
for (int k = sz - 1; k > 0; k--) {
data[k] = f(data[2 * k + 0], data[2 * k + 1]);
}
}
inline void propagate(int k) {
if (lazy[k] != OM0) {
lazy[2 * k + 0] = h(lazy[2 * k + 0], lazy[k]);
lazy[2 * k + 1] = h(lazy[2 * k + 1], lazy[k]);
data[k] = reflect(k);
lazy[k] = OM0;
}
}
inline Monoid reflect(int k) {
return lazy[k] == OM0 ? data[k] : g(data[k], lazy[k]);
}
inline void recalc(int k) {
while (k >>= 1) data[k] = f(reflect(2 * k + 0), reflect(2 * k + 1));
}
inline void thrust(int k) {
for (int i = height; i > 0; i--) propagate(k >> i);
}
void update(int a, int b, const OperatorMonoid& x) {
thrust(a += sz);
thrust(b += sz - 1);
for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
if (l & 1) lazy[l] = h(lazy[l], x), ++l;
if (r & 1) --r, lazy[r] = h(lazy[r], x);
}
recalc(a);
recalc(b);
}
Monoid query(int a, int b) {
thrust(a += sz);
thrust(b += sz - 1);
Monoid L = M1, R = M1;
for (int l = a, r = b + 1; l < r; l >>= 1, r >>= 1) {
if (l & 1) L = f(L, reflect(l++));
if (r & 1) R = f(reflect(--r), R);
}
return f(L, R);
}
Monoid operator[](const int& k) {
return query(k, k + 1);
}
template< typename C >
int find_subtree(int a, const C& check, Monoid& M, bool type) {
while (a < sz) {
propagate(a);
Monoid nxt = type ? f(reflect(2 * a + type), M) : f(M, reflect(2 * a + type));
if (check(nxt)) a = 2 * a + type;
else M = nxt, a = 2 * a + 1 - type;
}
return a - sz;
}
template< typename C >
int find_first(int a, const C& check) {
Monoid L = M1;
if (a <= 0) {
if (check(f(L, reflect(1)))) return find_subtree(1, check, L, false);
return -1;
}
thrust(a + sz);
int b = sz;
for (a += sz, b += sz; a < b; a >>= 1, b >>= 1) {
if (a & 1) {
Monoid nxt = f(L, reflect(a));
if (check(nxt)) return find_subtree(a, check, L, false);
L = nxt;
++a;
}
}
return -1;
}
template< typename C >
int find_last(int b, const C& check) {
Monoid R = M1;
if (b >= sz) {
if (check(f(reflect(1), R))) return find_subtree(1, check, R, true);
return -1;
}
thrust(b + sz - 1);
int a = sz;
for (b += sz; a < b; a >>= 1, b >>= 1) {
if (b & 1) {
Monoid nxt = f(reflect(--b), R);
if (check(nxt)) return find_subtree(b, check, R, true);
R = nxt;
}
}
return -1;
}
};
class KMP {
public:
vector<ll> table;
vector<ll> Pattern;
KMP(vector<ll> a) {
build(a);
}
void build(vector<ll> a) {
Pattern = a;
table = vector<ll>(a.size() + 1, -1);
int j = -1;
for (int i = 0; i < a.size(); ++i) {
while (j >= 0 && Pattern[i] != Pattern[j]) {
j = table[j];
}
table[i + 1] = ++j;
}
return;
}
vector<ll> search(vector<ll> a) {
vector<ll> ans;
for (int i = 0, k = 0; i < a.size(); ++i) {
while (k >= 0 && a[i] != Pattern[k]) k = table[k];
++k;
if (k >= Pattern.size()) {
ans.push_back(i - Pattern.size() + 1);
k = table[k];
}
}
return ans;
}
};
void init() {
iostream::sync_with_stdio(false);
cout << fixed << setprecision(20);
}
#define int ll
template< typename flow_t, typename cost_t >
struct PrimalDual {
const cost_t INF;
struct edge {
int to;
flow_t cap;
cost_t cost;
int rev;
bool isrev;
};
vector< vector< edge > > graph;
vector< cost_t > potential, min_cost;
vector< int > prevv, preve;
PrimalDual(int V) : graph(V), INF(numeric_limits< cost_t >::max()) {}
void add_edge(int from, int to, flow_t cap, cost_t cost) {
graph[from].emplace_back(edge{ to, cap, cost, (int)graph[to].size(), false });
graph[to].emplace_back(edge{ from, 0, -cost, (int)graph[from].size() - 1, true });
}
cost_t min_cost_flow(int s, int t, flow_t f) {
int V = (int)graph.size();
cost_t ret = 0;
using Pi = pair< cost_t, int >;
priority_queue< Pi, vector< Pi >, greater< Pi > > que;
potential.assign(V, 0);
preve.assign(V, -1);
prevv.assign(V, -1);
while (f > 0) {
min_cost.assign(V, INF);
que.emplace(0, s);
min_cost[s] = 0;
while (!que.empty()) {
Pi p = que.top();
que.pop();
if (min_cost[p.second] < p.first) continue;
for (int i = 0; i < graph[p.second].size(); i++) {
edge& e = graph[p.second][i];
cost_t nextCost = min_cost[p.second] + e.cost + potential[p.second] - potential[e.to];
if (e.cap > 0 && min_cost[e.to] > nextCost) {
min_cost[e.to] = nextCost;
prevv[e.to] = p.second, preve[e.to] = i;
que.emplace(min_cost[e.to], e.to);
}
}
}
if (min_cost[t] == INF) return -1;
for (int v = 0; v < V; v++) potential[v] += min_cost[v];
flow_t addflow = f;
for (int v = t; v != s; v = prevv[v]) {
addflow = min(addflow, graph[prevv[v]][preve[v]].cap);
}
f -= addflow;
ret += addflow * potential[t];
for (int v = t; v != s; v = prevv[v]) {
edge& e = graph[prevv[v]][preve[v]];
e.cap -= addflow;
graph[v][e.rev].cap += addflow;
}
}
return ret;
}
void output() {
for (int i = 0; i < graph.size(); i++) {
for (auto& e : graph[i]) {
if (e.isrev) continue;
auto& rev_e = graph[e.to][e.rev];
cout << i << "->" << e.to << " (flow: " << rev_e.cap << "/" << rev_e.cap + e.cap << ")" << endl;
}
}
}
};
int modpow(int a, int b, int p) {
int ans = 1;
while (b != 0) {
if (b % 2) {
ans *= a;
ans %= p;
}
a *= a;
a %= p;
b /= 2;
}
return ans;
}
int state = 0;
std::pair<ll, ll> baby[100010];
ll modlog(ll x, ll y, const ll p) {
ll H = sqrt(p) + 1;
for (ll b = 0, xby = y; b < H; b++, xby = (xby * x) % p) {
baby[b] = std::make_pair(xby, b);
}
std::sort(baby, baby + H);
state = 1;
ll xH = 1;
for (int i = 0; i < H; ++i) {
xH = (xH * x) % p;
}
for (ll a = 1, xaH = xH; a <= H; a++, xaH = (xaH * xH) % p) {
auto it = std::lower_bound(baby, baby + H, std::make_pair(xaH + 1, 0LL));
if (it == baby) continue;
it--;
if (it->first == xaH) return a * H - it->second;
}
return -1;
}
#define int unsigned long long
int in[3000000];
int out[3000000];
int visited[3000000];
vector<int> vertexs[3000000];
vector<int> cost, height;
int memo;
pair<int, int> dp(int now, int back) {
visited[now] = 1;
vector<int> go;
int base = 0;
for (auto& x : vertexs[now]) {
if (x == back) continue;
pair<int, int> hoge = dp(x, now);
base += hoge.first;
go.push_back(hoge.second - hoge.first);
}
pair<int, int> ans = mp(1e18, 1e18);
sort(ALL(go));
if (back == -1) {
int tmp = base;
int now_in = in[now] + (int)go.size();
int now_out = out[now];
memo = tmp + cost[now] * max(now_in, now_out);
for (int q = 0; q < go.size(); ++q) {
now_in--;
now_out++;
tmp += go[q];
memo = min(memo, tmp + cost[now] * max(now_in, now_out));
}
}
else {
{
int tmp = base;
int now_in = in[now] + (int)go.size();
int now_out = out[now] + 1LL;
ans.first = tmp + cost[now] * max(now_in, now_out);
for (int q = 0; q < go.size(); ++q) {
now_in--;
now_out++;
tmp += go[q];
ans.first = min(ans.first, tmp + cost[now] * max(now_in, now_out));
}
}
{
int tmp = base;
int now_in = in[now] + (int)go.size() + 1LL;
int now_out = out[now];
ans.second = tmp + cost[now] * max(now_in, now_out);
for (int q = 0; q < go.size(); ++q) {
now_in--;
now_out++;
tmp += go[q];
ans.second = min(ans.second, tmp + cost[now] * max(now_in, now_out));
}
}
}
return ans;
}
int grid[1000][1000];
void solve() {
int n;
cin >> n;
REP(i, n) {
REP(q, n) {
int x = i - q;
int y = i + q;
x += n;
y %= n;
x %= n;
grid[x][y] = i + 1;
}
}
REP(i, n) {
REP(q, n) {
cout << grid[i][q] << " ";
}
cout << endl;
}
}
#undef int
int main() {
init();
solve();
}