結果
| 問題 | No.3737 Quiz Time |
| コンテスト | |
| ユーザー |
 fact
|
| 提出日時 | 2026-09-19 15:53:04 |
| 言語 | C++23(gcc16) (gcc 16.1.0 + boost 1.92.0 + ACL) |
| 結果 |
AC
不安定
|
| 実行時間 | 201 ms / 2,000 ms |
| + 3µs | |
| コード長 | 39,806 bytes |
| 記録 | |
| コンパイル時間 | 6,732 ms |
| コンパイル使用メモリ | 451,848 KB |
| 実行使用メモリ | 9,920 KB |
| 平均クエリ数 | 84.22 |
| 最終ジャッジ日時 | 2026-09-19 15:53:21 |
| 合計ジャッジ時間 | 9,692 ms |
|
ジャッジサーバーID （参考情報） |
judge3_0 / <nil> |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 1 |
| other | AC * 50 |
ソースコード
#include"bits/stdc++.h"
#include"atcoder/all"
using namespace atcoder;
#pragma GCC target("avx2,fma")
#pragma GCC optimize("Ofast")
#pragma GCC optimize("unroll-loops")
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx,avx,tune=native")
using namespace std;
using ll = long long;
using vl = vector<ll>;
using vvl = vector<vl>;
using vvvl = vector<vvl>;
using vvvvl = vector<vvvl>;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using vvvvi = vector<vvvi>;
typedef pair<ll, ll> P;
typedef pair<long double, ll> Pd;
typedef tuple<ll, ll, ll> PP;
typedef tuple<ll, ll, ll, ll> PPP;
using vs = vector<string>;
using vvs = vector<vs>;
using vvvs = vector<vvs>;
using vp = vector<P>;
using vvp = vector<vp>;
using vvvp = vector<vvp>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vvvb = vector<vvb>;
#define lb(v, k) (lower_bound(all(v), (k)) - v.begin())
#define ub(v, k) (upper_bound(all(v), (k)) - v.begin())
#define eb emplace_back
#define fi first
#define se second
#define pq(T) priority_queue<T>
#define pqr(T) priority_queue<T, vector<T>, greater<T>>
#define pcount(i) __builtin_popcountll(i)
#define rep(i, n) for (ll i = 0; i < (ll)(n); i++)
#define repi(i, a, b) for (ll i = (ll)(a); i < (ll)(b); i++)
#define all(a) (a).begin(), (a).end()
#define rll(a) (a).rbegin(), (a).rend()
#define double long double
#define yesno(i) if(i)cout<<"yes"<<endl;else cout<<"no"<<endl;
#define YesNo(i) if(i)cout<<"Yes"<<endl;else cout<<"No"<<endl;
#define YESNO(i) if(i)cout<<"YES"<<endl;else cout<<"NO"<<endl;
#define pb push_back
#define cinvec(x) \
for (ll hfuaig = 0; hfuaig < x.size(); hfuaig++) \
{ \
cin >> x.at(hfuaig); \
}
#define coutvece(x) \
for (ll hfuaig = 0; hfuaig < x.size(); hfuaig++) \
{ \
cout << x.at(hfuaig) << endl; \
}
#define coutvec(x) \
for (ll hfuaig = 0; hfuaig < x.size(); hfuaig++) \
{ \
cout << x.at(hfuaig) << ' '; \
}\
cout << endl;
vl dx = {-1,1 ,0 ,0 ,-1, 1, -1, 1};
vl dy = {0 ,0 ,-1,1 ,-1, -1, 1, 1};
pair<ll, ll> dxy(pair<ll, ll> a, ll i){
return make_pair(a.fi + dx[i], a.se + dy[i]);
}
template <typename T>
bool chmax(T &a, const T& b){
if(a < b){
a = b;
return true;
}
return false;
}
template <typename T>
bool chmin(T &a, const T& b){
if(a > b){
a = b;
return true;
}
return false;
}
ll mod = 998244353;
int modd = 998244353;
const ll Mod = 1000000007;
const ll inf = 999999999999999999LL;
const int INF = 999999999;
using mint = modint998244353;
using mmint = modint1000000007;
using intm = static_modint<1000000009>;
using vm = vector<mint>;
using vvm = vector<vm>;
using vvvm = vector<vvm>;
using vvvvm = vector<vvvm>;
using vvvvvm = vector<vvvvm>;
using vmm = vector<mmint>;
using vvmm = vector<vmm>;
using vvvmm = vector<vvmm>;
ll mygcd(ll A, ll B){
if(A == -1)return B;
if(B == -1)return A;
if(B == 0 || A == 0){
return A ^ B;
}
if(A % B == 0){
return B;
}
else{
return mygcd(B, A % B);
}
}
ll mylcm(ll A, ll B){
if(A == -1){
return B;
}
if(B == -1){
return A;
}
return A / mygcd(A, B) * B;
}
typedef struct Point_Coordinates {
double x, y;
} point;
typedef struct Point_Coordinatesll {
ll x, y;
} pointl;
long long modpow(long long a, long long n, long long mo) {
long long res = 1;
while (n > 0) {
if (n & 1) res = res * a % mo;
a = a * a % mo;
n >>= 1;
}
return res % mo;
}
//円の位置関係
bool isd(double a, double b, double c){
if(c > (a + b) * (a + b)){
return false;
}
if(c == (a + b) * (a + b)){
return true;
}
if(abs(a - b) * abs(a - b) < c && c < (a + b) * (a + b)){
return true;
}
if(c == abs(a - b) * abs(a - b)){
return true;
}
if(c < abs(a - b) * abs(a - b)){
return false;
}
return true;
}
const int MAX = 201;
int MOD1 = mod;
ll fact[MAX], inv_fact[MAX], inv[MAX], perm[MAX];
void init() {
MOD1 = mod;
// 初期値設定と1はじまりインデックスに直す
fact[0] = 1;
fact[1] = 1;
inv[0] = 1;
inv[1] = 1;
inv_fact[0] = 1;
inv_fact[1] = 1;
// メモの計算
repi(i, 2, MAX){
// 階乗
fact[i] = fact[i - 1] * i % MOD1;
// 逆元
inv[i] = MOD1 - inv[MOD1%i] * (MOD1 / i) % MOD1;
// 逆元の階乗
inv_fact[i] = inv_fact[i - 1] * inv[i] % MOD1;
}
perm[0] = 1;
rep(i, MAX - 1){
perm[i + 1] = ((ll)(i + 1) * perm[i]) % MOD1;
}
}
ll nck(int n, int k) {
if (n < k) return 0; // 例外処理
if (n < 0 || k < 0) return 0; // 例外処理
if(k == 0)return 1;
ll x = fact[n]; // n!の計算
ll y = inv_fact[n-k]; // (n-k)!の計算
ll z = inv_fact[k]; // k!の計算
return x * ((y * z) % MOD1) % MOD1; //二項係数の計算
}
ll npk(ll n, ll k){
return (nck(n, k) * perm[k]) % MOD1;
}
ll nhk(ll n, ll k){
return nck(n + k - 1, k);
}
struct graph{
ll N;
vvp G;
vl dis;
vl prev;
graph(ll n) : N(n){
G.resize(n);
}
void push(ll a, ll b){
G[a].push_back({b, 1});
}
void push(ll a, ll b, ll c){
G[a].push_back({b, c});
}
vl dijkstra(ll i){
dis.assign(N, inf);
prev.assign(N, -1);
priority_queue<P, vector<P>, greater<P>> piq; // 「仮の最短距離, 頂点」が小さい順に並ぶ
dis[i] = 0;
piq.emplace(dis[i], i);
while (!piq.empty()) {
P p = piq.top();
piq.pop();
ll v = p.second;
if (dis[v] < p.first) { // 最短距離で無ければ無視
continue;
}
for (auto &e : G[v]) {
if (dis[e.fi] > dis[v] + e.se) { // 最短距離候補なら priority_queue に追加
dis[e.fi] = dis[v] + e.se;
prev[e.fi] = v;
piq.emplace(dis[e.fi], e.fi);
}
}
}
return dis;
}
vl get_path(ll t){
vl path;
for (ll cur = t; cur != -1; cur = prev[cur]) {
path.push_back(cur);
}
reverse(path.begin(), path.end()); // 逆順なのでひっくり返す
return path;
}
};
struct BIT {
private:
vector<ll> bit;
ll N;
public:
BIT(ll size) {
N = size;
bit.resize(N + 1, 0);
}
// 一点更新です
void add(ll a, ll w) {
for (int x = a; x <= N; x += x & -x) bit[x] += w;
}
// 1~Nまでの和を求める。
ll sum(ll a) {
ll ret = 0;
for (ll x = a; x > 0; x -= x & -x) ret += bit[x];
return ret;
}
};
//転倒数ライブラリ 1-indexed!!
ll numfalls(vl &A){
ll ans = 0;
ll N = A.size();
BIT b(N);
rep(i, N){
ans += i - b.sum(A.at(i));
b.add(A.at(i), 1);
}
return ans;
}
//#define _GLIBCXX_DEBUG
#define mint998 modint998244353
#define mint107 modint1000000007
//約数列挙
vector<long long> div(long long n) {
vector<long long> ret;
set<ll> re;
ll N = sqrt(n) + 1;
for (long long i = 1; i <= N; i++) {
if (n % i == 0) {
re.insert(n / i);
re.insert(i);
}
}
for(auto value :re){
ret.push_back(value);
}
return ret;
}
ll digit_sum(ll X){
ll ans = 0;
while(X > 0){
ans += X%10;
X/=10;
}
return ans;
}
void xypress(vl &A){
vl B = A;
sort(all(B));
B.erase(unique(B.begin(), B.end()), B.end());
vector<ll> res(A.size());
for (int i = 0; i < A.size(); ++i) {
res[i] = lower_bound(B.begin(), B.end(), A[i]) - B.begin();
}
A = res;
}
//素数列挙
std::vector<ll> prime( const ll N )
{
std::vector<bool> is_prime( N + 1 );
for( ll i = 0; i <= N; i++ )
{
is_prime[ i ] = true;
}
std::vector<ll> P;
for( ll i = 2; i <= N; i++ )
{
if( is_prime[ i ] )
{
for( ll j = 2 * i; j <= N; j += i )
{
is_prime[ j ] = false;
}
P.push_back( i );
}
}
return P;
}
//mod m での逆元
long long modinv(long long a, long long m) {
long long b = m, u = 1, v = 0;
while (b) {
long long t = a / b;
a -= t * b; swap(a, b);
u -= t * v; swap(u, v);
}
u %= m;
if (u < 0) u += m;
return u;
}
//mod 998244353での割り算
ll inve(ll a, ll b){
a %= mod;
return (a * modinv(b, mod) % mod);
}
vl vecsum(vl x){
vl s = {0};
rep(i, x.size()){
s.push_back(s.back() + x.at(i));
}
return s;
}
const int N_MAX = 10;
ll spf[N_MAX]; // smallest prime factors
void prepare_factorize() {
rep(i, N_MAX) spf[i] = i;
for (int p = 2; p * p <= N_MAX; p++) {
for (int i = p; i < N_MAX; i += p) {
if (spf[i] == i) spf[i] = p;
}
}
}
// 素因数分解
// その素因数が何個あるかのmapを返す
map<ll, ll> allprime(ll n) {
map<ll, ll> c;
while (n != 1) {
ll p = spf[n];
while (n % p == 0) {
n /= p;
c[p]++;
}
}
return c;
}///////////////////////////////////
vl prime2(ll n) {
vl c(500);
while (n != 1) {
ll p = spf[n];
while (n % p == 0) {
n /= p;
c[p]++;
}
}
return c;
}///////////////////////////////////
vector<ll> primes(ll n){
set<ll> c;
for(ll i = 2;i * i <= n;i++){
if(n % i == 0)c.insert(i);
while(n % i == 0){
n /= i;
}
}
if(n != 1){
c.insert(n);
}
vl d;
for(auto a : c){
d.push_back(a);
}
return d;
}
vector<ll> SA_IS(vector<ll> str, ll var) {
if(str.size() == 1) {
vector<ll> ret(1,0);
return ret;
}
str.push_back(0);
ll si = str.size();
vector<ll> st(var, 0), en(var, 0);
vector<ll> SL(si, 0); //s..0, l..1
vector<ll> SA(si, -1);
vector<ll> LMS;
vector<ll> is_LMS(si, -1);
rep(i,str.size()) en[str[i]]++;
for(ll i = 1; i < var; i++) en[i] += en[i-1];
for(ll i = 1; i < var; i++) st[i] = en[i-1];
SL[str.size()-1] = 0;
for(ll i = str.size()-2; i >= 0; i--) {
if(str[i] == str[i+1]) {
SL[i] = SL[i+1];
continue;
}
if(str[i] > str[i+1]) SL[i] = 1;
else SL[i] = 0;
}
for(ll i = 1; i < str.size(); i++) {
if(SL[i] == 0 && SL[i-1] == 1) {
SA[--en[str[i]]] = i;
LMS.push_back(i);
is_LMS[i] = 1;
}
}
rep(i,var-1) en[i] = st[i+1];
en[var-1] = str.size();
rep(i,str.size()) if(SA[i] > 0 && SL[SA[i]-1] == 1) { SA[st[str[SA[i]-1]]++] = SA[i]-1; }
st[0] = 0;
for(ll i = 1; i < var; i++) st[i] = en[i-1];
for(ll i = 1; i < str.size(); i++) if(SA[i] != -1 && SL[SA[i]] == 0) { SA[i] = -1; }
for(ll i = str.size()-1; i >= 1; i--) if(SA[i] > 0 && SL[SA[i]-1] == 0) { SA[--en[str[SA[i]-1]]] = SA[i]-1; }
rep(i,var-1) en[i] = st[i+1];
en[var-1] = str.size();
ll counter = 0;
vector<ll> pre_sa, new_sa;
rep(i,SA.size()) if(is_LMS[SA[i]] != -1) {
is_LMS[SA[i]] = ++counter;
new_sa.clear();
for(ll j = SA[i]; j < SA.size(); j++) {
new_sa.push_back(str[j]);
if(j != SA[i] && is_LMS[j] != -1) {
break;
}
}
if(pre_sa == new_sa) {
is_LMS[SA[i]] = --counter;
}
pre_sa = new_sa;
}
vector<ll> new_str;
vector<ll> rev((ll)LMS.size()+1, 0);
counter = 0;
rep(i,is_LMS.size()) {
if(is_LMS[i] != -1) {
new_str.push_back(is_LMS[i]);
rev[counter++] = i;
}
}
vector<ll> rec = SA_IS(new_str, new_str.size()+1);
rep(i,SA.size()) SA[i] = -1;
for(ll i = rec.size()-1; i >= 0; i--) { SA[--en[str[rev[rec[i]]]]] = rev[rec[i]]; }
rep(i,var-1) en[i] = st[i+1];
en[var-1] = str.size();
rep(i,str.size()) if(SA[i] > 0 && SL[SA[i]-1] == 1) { SA[st[str[SA[i]-1]]++] = SA[i]-1; }
for(ll i = 1; i < str.size(); i++) if(SA[i] != -1 && SL[SA[i]] == 0) { SA[i] = -1; }
for(ll i = str.size()-1; i >= 1; i--) if(SA[i] > 0 && SL[SA[i]-1] == 0) { SA[--en[str[SA[i]-1]]] = SA[i]-1; }
SA.erase(SA.begin());
return SA;
}
int Judge(point &a, point &b, point &c, point &d) {
double s, t;
s = (a.x - b.x) * (c.y - a.y) - (a.y - b.y) * (c.x - a.x);
t = (a.x - b.x) * (d.y - a.y) - (a.y - b.y) * (d.x - a.x);
if (s * t > 0)
return false;
s = (c.x - d.x) * (a.y - c.y) - (c.y - d.y) * (a.x - c.x);
t = (c.x - d.x) * (b.y - c.y) - (c.y - d.y) * (b.x - c.x);
if (s * t > 0)
return false;
return true;
}
int Judgel(pointl &a, pointl &b, pointl &c, pointl &d) {
ll s, t;
s = (a.x - b.x) * (c.y - a.y) - (a.y - b.y) * (c.x - a.x);
t = (a.x - b.x) * (d.y - a.y) - (a.y - b.y) * (d.x - a.x);
if (s * t > 0)
return false;
s = (c.x - d.x) * (a.y - c.y) - (c.y - d.y) * (a.x - c.x);
t = (c.x - d.x) * (b.y - c.y) - (c.y - d.y) * (b.x - c.x);
if (s * t > 0)
return false;
return true;
}
double kyori(point &a, point &b){
double x = abs(a.x - b.x), y = abs(a.y - b.y);
return sqrt(x * x + y * y);
}
double eps = 1;
struct Edge {
ll to;
};
using Graph = vector<vector<Edge>>;
vector<ll> topo_sort(const Graph &G) { // bfs
vector<ll> ans;
ll n = (ll)G.size();
vector<ll> ind(n); // ind[i]: 頂点iに入る辺の数(次数)
for (ll i = 0; i < n; i++) { // 次数を数えておく
for (auto e : G[i]) {
ind[e.to]++;
}
}
queue<ll> que;
for (ll i = 0; i < n; i++) { // 次数が0の点をキューに入れる
if (ind[i] == 0) {
que.push(i);
}
}
while (!que.empty()) { // 幅優先探索
ll now = que.front();
ans.push_back(now);
que.pop();
for (auto e : G[now]) {
ind[e.to]--;
if (ind[e.to] == 0) {
que.push(e.to);
}
}
}
return ans;
}
struct LCA {
vector<vector<int>> parent; // parent[k][u]:= u の 2^k 先の親
vector<int> dist; // root からの距離
LCA(const Graph &G, int root = 0) { init(G, root); }
// 初期化
void init(const Graph &G, int root = 0) {
int V = G.size();
int K = 1;
while ((1 << K) < V) K++;
parent.assign(K, vector<int>(V, -1));
dist.assign(V, -1);
dfs(G, root, -1, 0);
for (int k = 0; k + 1 < K; k++) {
for (int v = 0; v < V; v++) {
if (parent[k][v] < 0) {
parent[k + 1][v] = -1;
} else {
parent[k + 1][v] = parent[k][parent[k][v]];
}
}
}
}
// 根からの距離と1つ先の頂点を求める
void dfs(const Graph &G, int v, int p, int d) {
parent[0][v] = p;
dist[v] = d;
for (auto e : G[v]) {
if (e.to != p) dfs(G, e.to, v, d + 1);
}
}
int query(int u, int v) {
if (dist[u] < dist[v]) swap(u, v); // u の方が深いとする
int K = parent.size();
// LCA までの距離を同じにする
for (int k = 0; k < K; k++) {
if ((dist[u] - dist[v]) >> k & 1) {
u = parent[k][u];
}
}
// 二分探索で LCA を求める
if (u == v) return u;
for (int k = K - 1; k >= 0; k--) {
if (parent[k][u] != parent[k][v]) {
u = parent[k][u];
v = parent[k][v];
}
}
return parent[0][u];
}
int get_dist(int u, int v) { return dist[u] + dist[v] - 2 * dist[query(u, v)]; }
bool is_on_path(int u, int v, int a) { return get_dist(u, a) + get_dist(a, v) == get_dist(u, v); }
};
struct matrix{
ll h, w;
vvl X;
matrix(ll H, ll W) : h(H), w(W){
init();
}
void init(){
X.assign(h, vl(w, 0));
}
void set(ll H, ll W, ll c){
X.at(H).at(W) = c;
}
ll get(ll H, ll W){
return X.at(H).at(W);
}
};
struct rollinghash{
__int128_t m = (1LL << 61) - 1;
__int128_t base;
string S;
int N;
vl h, sh, pw;
rollinghash(string x) : S(x), N((int)x.size()){
base = rand() % (m - 2) + 2;
st();
}
void st(){
h.assign(N + 1, 0);
sh.assign(N + 1, 0);
pw.assign(N + 1, 1);
for(int i = 0;i < N;i++){
pw.at(i + 1) = (__int128_t)pw.at(i) * base % m;
}
for(int i = 0;i < N;i++){
h.at(i + 1) = ((__int128_t)h.at(i) * base + (__int128_t)S.at(i)) % m;
}
for(int i = N - 1;i >= 0;i--){
sh.at(i) = ((__int128_t)sh.at(i + 1) * base + (__int128_t)S.at(i)) % m;
}
}
ll hash(int l, int r){
if(l == r){
return 0;
}
else if(l < r){
return (h.at(r) - (__int128_t)h.at(l) * pw.at(r - l) % m + m) % m;
}
else{
return (sh.at(r) - (__int128_t)sh.at(l) * pw.at(l - r) % m + m) % m;
}
}
ll range_hash(vector<pair<int, int>> p){
ll now = 0, ret = 0;
reverse(all(p));
for(int i = 0;i < p.size();i++){
ret += (__int128_t)hash(p.at(i).fi, p.at(i).se) * pw.at(now) % m;
ret %= m;
now += abs(p.at(i).fi - p.at(i).se);
}
return ret;
}
ll range_hash(vector<pair<ll, ll>> p){
ll now = 0, ret = 0;
reverse(all(p));
for(int i = 0;i < p.size();i++){
ret += (__int128_t)hash(p.at(i).fi, p.at(i).se) * pw.at(now) % m;
ret %= m;
now += abs(p.at(i).fi - p.at(i).se);
}
return ret;
}
};
class CentroidDecomposition
{
public:
int V;
vector<vector<ll> > G;
vector<bool> used;
//sz:重心分解後の最大部分木に含まれる頂点の数(自分を含める)
//par:重心分解後の親の頂点
vector<ll> sz, par;
//部分木のサイズを計算
void calcSize(ll u,ll p){
sz[u] = 1;
for(ll v : G[u]){
if(!used[v] && v != p){
calcSize(v,u);
sz[u] += sz[v];
}
}
}
void cdBuild(ll u,ll p){
calcSize(u,-1);
ll tot = sz[u];
bool ok = false;
ll pp = -1;
//いま見ている部分木での重心を見つける
while(!ok){
ok = true;
for(ll v : G[u]){
if(!used[v] && v != pp && 2*sz[v] > tot){
pp = u, u = v, ok = false;
break;
}
}
}
par[u] = p;
//何らかの操作
used[u] = true;
//深さ優先でたどる
for(ll v : G[u]){
if(!used[v]){
cdBuild(v,u);
}
}
}
CentroidDecomposition(ll node_size) : V(node_size), G(V), used(V, false)
, sz(V, 0), par(V, -1){}
void add_edge(ll u,ll v){
G[u].push_back(v), G[v].push_back(u);
}
void build(){
cdBuild(0,-1);
}
};
template <typename T, typename S>
istream &operator>>(istream &a, pair<T, S> &b){
a >> b.fi >> b.se;
return a;
}
template <typename T, typename S>
ostream& operator<<(ostream& os, const pair<T, S>& p) {
return os << p.first << ' ' << p.second;
}
template <typename T>
istream &operator>>(istream &a, vector<T> &b){
rep(i, b.size()){
a >> b.at(i);
}
return a;
}
template <typename T>
ostream& operator<<(ostream& os, const vector<T>& v) {
for (int i = 0; i < (int)v.size(); i++) {
if (i) os << ' ';
os << v[i];
}
return os;
}
template <typename T>
ostream &operator<<(ostream &a, vector<vector<T>> &b){
rep(i, b.size()){
a << b.at(i);
if(i != b.size() - 1){
a<<endl;
}
}
return a;
}
template<typename T>
istream &operator>>(istream &a, set<T> &b){
T tmp;
a >> tmp;
b.insert(tmp);
return a;
}
void scan(){}
template <class T, class... S>
void scan(T &head, S &... plus){
cin >> head;
scan(plus...);
}
void out(){}
template <class T, class... S>
void out(const T &head, const S &... plus){
cout << head << endl;
out(plus...);
}
//行列の乗算
vvl matrix_mult(vvl X, vvl Y) {
vvl Z(X.size(), vl(Y[0].size()));
rep(i, X.size()) {
rep(k, Y.size()) {
rep(j, Y[0].size()) {
Z[i][j] = (Z[i][j] + X[i][k] * Y[k][j]) % mod;
}
}
}
return Z;
}
//A^nの計算
vvl matrix_pow(vvl A, ll n) {
vvl B(A.size(), vl(A[0].size()));
//単位行列でBを初期化
rep(i, B.size()) {
B[i][i] = 1;
}
while (n>0) {
if (n & 1) { B = matrix_mult(B, A); }
A = matrix_mult(A, A);
n = n >> 1;
}
return B;
}
template< typename T >
struct FormalPowerSeries : vector< T > {
using vector< T >::vector;
using P = FormalPowerSeries;
P pre(int deg) const {
return P(begin(*this), begin(*this) + min((int) this->size(), deg));
}
P rev(int deg = -1) const {
P ret(*this);
if(deg != -1) ret.resize(deg, T(0));
reverse(begin(ret), end(ret));
return ret;
}
void shrink() {
while(this->size() && this->back() == T(0)) this->pop_back();
}
P operator+(const P &r) const { return P(*this) += r; }
P operator+(const T &v) const { return P(*this) += v; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator-(const T &v) const { return P(*this) -= v; }
P operator*(const P &r) const { return P(*this) *= r; }
P operator*(const T &v) const { return P(*this) *= v; }
P operator/(const P &r) const { return P(*this) /= r; }
P operator%(const P &r) const { return P(*this) %= r; }
P &operator+=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] += r[i];
return *this;
}
P &operator-=(const P &r) {
if(r.size() > this->size()) this->resize(r.size());
for(int i = 0; i < r.size(); i++) (*this)[i] -= r[i];
return *this;
}
P &operator*=(const P &r) {
if(this->empty() || r.empty()) {
this->clear();
return *this;
}
auto ret = convolution(*this, r);
return *this = {begin(ret), end(ret)};
}
P &operator/=(const P &r) {
if(this->size() < r.size()) {
this->clear();
return *this;
}
int n = this->size() - r.size() + 1;
return *this = (rev().pre(n) * r.rev().inv(n)).pre(n).rev(n);
}
P &operator%=(const P &r) {
return *this -= *this / r * r;
}
// https://judge.yosupo.jp/problem/division_of_polynomials
pair< P, P > div_mod(const P &r) {
P q = *this / r;
return make_pair(q, *this - q * r);
}
P operator-() const {
P ret(this->size());
for(int i = 0; i < this->size(); i++) ret[i] = -(*this)[i];
return ret;
}
P &operator+=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] += r;
return *this;
}
P &operator-=(const T &r) {
if(this->empty()) this->resize(1);
(*this)[0] -= r;
return *this;
}
P &operator*=(const T &v) {
for(int i = 0; i < this->size(); i++) (*this)[i] *= v;
return *this;
}
P dot(P r) const {
P ret(min(this->size(), r.size()));
for(int i = 0; i < ret.size(); i++) ret[i] = (*this)[i] * r[i];
return ret;
}
P operator>>(int sz) const {
if(this->size() <= sz) return {};
P ret(*this);
ret.erase(ret.begin(), ret.begin() + sz);
return ret;
}
P operator<<(int sz) const {
P ret(*this);
ret.insert(ret.begin(), sz, T(0));
return ret;
}
T operator()(T x) const {
T r = 0, w = 1;
for(auto &v : *this) {
r += w * v;
w *= x;
}
return r;
}
P diff() const {
const int n = (int) this->size();
P ret(max(0, n - 1));
for(int i = 1; i < n; i++) ret[i - 1] = (*this)[i] * T(i);
return ret;
}
P integral() const {
const int n = (int) this->size();
P ret(n + 1);
ret[0] = T(0);
for(int i = 0; i < n; i++) ret[i + 1] = (*this)[i] / T(i + 1);
return ret;
}
// https://judge.yosupo.jp/problem/inv_of_formal_power_series
// F(0) must not be 0
P inv(int deg = -1) const {
assert(((*this)[0]) != T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
P ret({T(1) / (*this)[0]});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + ret - ret * ret * pre(i << 1)).pre(i << 1);
}
return ret.pre(deg);
}
// https://judge.yosupo.jp/problem/log_of_formal_power_series
// F(0) must be 1
P log(int deg = -1) const {
assert((*this)[0] == T(1));
const int n = (int) this->size();
if(deg == -1) deg = n;
return (this->diff() * this->inv(deg)).pre(deg - 1).integral();
}
// https://judge.yosupo.jp/problem/sqrt_of_formal_power_series
P sqrt(int deg = -1, const function< T(T) > &get_sqrt = [](T) { return T(1); }) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
if((*this)[0] == T(0)) {
for(int i = 1; i < n; i++) {
if((*this)[i] != T(0)) {
if(i & 1) return {};
if(deg - i / 2 <= 0) break;
auto ret = (*this >> i).sqrt(deg - i / 2, get_sqrt);
if(ret.empty()) return {};
ret = ret << (i / 2);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return P(deg, 0);
}
auto sqr = T(get_sqrt((*this)[0]));
if(sqr * sqr != (*this)[0]) return {};
P ret{sqr};
T inv2 = T(1) / T(2);
for(int i = 1; i < deg; i <<= 1) {
ret = (ret + pre(i << 1) * ret.inv(i << 1)) * inv2;
}
return ret.pre(deg);
}
P sqrt(const function< T(T) > &get_sqrt, int deg = -1) const {
return sqrt(deg, get_sqrt);
}
// https://judge.yosupo.jp/problem/exp_of_formal_power_series
// F(0) must be 0
P exp(int deg = -1) const {
if(deg == -1) deg = this->size();
assert((*this)[0] == T(0));
const int n = (int) this->size();
if(deg == -1) deg = n;
P ret({T(1)});
for(int i = 1; i < deg; i <<= 1) {
ret = (ret * (pre(i << 1) + T(1) - ret.log(i << 1))).pre(i << 1);
}
return ret.pre(deg);
}
// https://judge.yosupo.jp/problem/pow_of_formal_power_series
P pow(int64_t k, int deg = -1) const {
const int n = (int) this->size();
if(deg == -1) deg = n;
if(k == 0) {
P ret(deg, T(0));
ret[0] = T(1);
return ret;
}
for(int i = 0; i < n; i++) {
if(i * k > deg) return P(deg, T(0));
if((*this)[i] != T(0)) {
T rev = T(1) / (*this)[i];
P ret = (((*this * rev) >> i).log() * k).exp() * ((*this)[i].pow(k));
ret = (ret << (i * k)).pre(deg);
if(ret.size() < deg) ret.resize(deg, T(0));
return ret;
}
}
return *this;
}
// https://yukicoder.me/problems/no/215
P mod_pow(int64_t k, P g) const {
P modinv = g.rev().inv();
auto get_div = [&](P base) {
if(base.size() < g.size()) {
base.clear();
return base;
}
int n = base.size() - g.size() + 1;
return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);
};
P x(*this), ret{1};
while(k > 0) {
if(k & 1) {
ret *= x;
ret -= get_div(ret) * g;
ret.shrink();
}
x *= x;
x -= get_div(x) * g;
x.shrink();
k >>= 1;
}
return ret;
}
// https://judge.yosupo.jp/problem/polynomial_taylor_shift
P taylor_shift(T c) const {
int n = (int) this->size();
vector< T > fact(n), rfact(n);
fact[0] = rfact[0] = T(1);
for(int i = 1; i < n; i++) fact[i] = fact[i - 1] * T(i);
rfact[n - 1] = T(1) / fact[n - 1];
for(int i = n - 1; i > 1; i--) rfact[i - 1] = rfact[i] * T(i);
P p(*this);
for(int i = 0; i < n; i++) p[i] *= fact[i];
p = p.rev();
P bs(n, T(1));
for(int i = 1; i < n; i++) bs[i] = bs[i - 1] * c * rfact[i] * fact[i - 1];
p = (p * bs).pre(n);
p = p.rev();
for(int i = 0; i < n; i++) p[i] *= rfact[i];
return p;
}
};
template< typename Mint >
using FPS = FormalPowerSeries< Mint >;
// Bostan-Mori
// find [x^N] P(x)/Q(x), O(K log K log N)
// deg(Q(x)) = K, deg(P(x)) < K, Q[0] = 1
template <typename mint> mint BostanMori(const FPS<mint> &P, const FPS<mint> &Q, long long N) {
assert(!P.empty() && !Q.empty());
if (N == 0) return P[0] / Q[0];
int qdeg = (int)Q.size();
FPS<mint> P2{P}, minusQ{Q};
P2.resize(qdeg - 1);
for (int i = 1; i < (int)Q.size(); i += 2) minusQ[i] = -minusQ[i];
P2 *= minusQ;
FPS<mint> Q2 = Q * minusQ;
FPS<mint> S(qdeg - 1), T(qdeg);
for (int i = 0; i < (int)S.size(); ++i) {
S[i] = (N % 2 == 0 ? P2[i * 2] : P2[i * 2 + 1]);
}
for (int i = 0; i < (int)T.size(); ++i) {
T[i] = Q2[i * 2];
}
return BostanMori(S, T, N >> 1);
}
// Union-Find, we can undo
struct UnionFind {
// core member
vector<int> par;
stack<pair<int,int>> history;
// constructor
UnionFind() {}
UnionFind(int n) : par(n, -1) { }
void init(int n) { par.assign(n, -1); }
// core methods
int root(int x) {
if (par[x] < 0) return x;
else return root(par[x]);
}
bool same(int x, int y) {
return root(x) == root(y);
}
bool merge(int x, int y) {
x = root(x), y = root(y);
history.emplace(x, par[x]);
history.emplace(y, par[y]);
if (x == y) return false;
if (par[x] > par[y]) swap(x, y); // merge technique
par[x] += par[y];
par[y] = x;
return true;
}
int size(int x) {
return -par[root(x)];
}
// 1-step undo
void undo() {
for (int iter = 0; iter < 2; ++iter) {
par[history.top().first] = history.top().second;
history.pop();
}
}
// erase history
void snapshot() {
while (!history.empty()) history.pop();
}
// all rollback
void rollback() {
while (!history.empty()) undo();
}
// debug
friend ostream& operator << (ostream &s, UnionFind uf) {
map<int, vector<int>> groups;
for (int i = 0; i < uf.par.size(); ++i) {
int r = uf.root(i);
groups[r].push_back(i);
}
for (const auto &it : groups) {
s << "group: ";
for (auto v : it.second) s << v << " ";
s << endl;
}
return s;
}
};
istream &operator>>(istream &a, mint &b){
ll tmp;
a >> tmp;
b = tmp;
return a;
}
ostream& operator<<(ostream& os, const mint& x) {
return os << x.val();
}
istream &operator>>(istream &a, mmint &b){
ll tmp;
a >> tmp;
b = tmp;
return a;
}
ostream& operator<<(ostream& os, const mmint& x) {
return os << x.val();
}
#line 1 "math/number-theory/generalized-floor-sum-pq-le-2.hpp"
// 一般化 floor sum (p+q<=2) のうち (0,1),(1,1),(0,2) をまとめて求める。
// ans_01 = Σ floor((a i + b)/m), ans_11 = Σ i*floor((a i + b)/m), ans_02 = Σ floor((a i + b)/m)^2。
// n>=0, m>0 を仮定する。a,b は負でもよい。
// 計算量 O(log m)。
#include <cassert>
#include <type_traits>
template <class T> struct GeneralizedFloorSumPQLe2Result {
T ans_01;
T ans_11;
T ans_02;
};
namespace generalized_floor_sum_pq_le_2_internal {
template <class T> struct is_integral : std::is_integral<T> {};
#ifdef __SIZEOF_INT128__
template <> struct is_integral<__int128_t> : std::true_type {};
template <> struct is_integral<__uint128_t> : std::true_type {};
#endif
template <class T> struct is_signed : std::is_signed<T> {};
#ifdef __SIZEOF_INT128__
template <> struct is_signed<__int128_t> : std::true_type {};
template <> struct is_signed<__uint128_t> : std::false_type {};
#endif
template <class T> T floor_div(T x, T y) {
assert(y > 0);
if constexpr (is_signed<T>::value) {
T q = x / y;
T r = x % y;
if (r < 0)
--q;
return q;
} else {
return x / y;
}
}
template <class T> T floor_mod(T x, T y) {
assert(y > 0);
if constexpr (is_signed<T>::value) {
T r = x % y;
if (r < 0)
r += y;
return r;
} else {
return x % y;
}
}
// Σ_{i=0}^{n-1} i = n(n-1)/2
template <class T> T sum_0_to_n_minus_1(T n) {
if (n == 0)
return 0;
if ((n & 1) == 0)
return (n / 2) * (n - 1);
return n * ((n - 1) / 2);
}
// Σ_{i=0}^{n-1} i^2 = (n-1)n(2n-1)/6
template <class T> T sum_0_to_n_minus_1_sq(T n) {
if (n == 0)
return 0;
T a = n - 1, b = n, c = 2 * n - 1;
if ((a % 2) == 0)
a /= 2;
else if ((b % 2) == 0)
b /= 2;
else
c /= 2;
if ((a % 3) == 0)
a /= 3;
else if ((b % 3) == 0)
b /= 3;
else
c /= 3;
return a * b * c;
}
template <class T> T sum_range(T l, T r) {
// Σ_{i=l}^{r} i
if (l > r)
return 0;
T cnt = r - l + 1;
T s = l + r;
if ((s & 1) == 0)
s /= 2;
else
cnt /= 2;
return s * cnt;
}
template <class Int> struct Result {
Int ans_01;
Int ans_11;
Int ans_02;
};
template <class Int> Result<Int> solve(Int n, Int m, Int a, Int b) {
if constexpr (is_signed<Int>::value)
assert(n >= 0);
assert(m > 0);
if (n == 0)
return {0, 0, 0};
const Int qa = floor_div(a, m);
a = floor_mod(a, m);
const Int qb = floor_div(b, m);
b = floor_mod(b, m);
if constexpr (is_signed<Int>::value) {
assert(a >= 0);
assert(b >= 0);
}
assert(a < m);
assert(b < m);
Result<Int> base = {0, 0, 0};
if (a != 0) {
const Int y_max = (a * n + b) / m;
if (y_max != 0) {
const Int x_max = y_max * m - b;
const Int t = (x_max + a - 1) / a; // ceil(x_max / a)
const Int b2 = (a - (x_max % a)) % a;
const auto rec = solve(y_max, a, m, b2);
const Int head_01 = rec.ans_01;
const Int head_11 = ((2 * t - 1) * rec.ans_01 - rec.ans_02) / 2;
const Int head_02 = (2 * y_max - 1) * rec.ans_01 - 2 * rec.ans_11;
const Int tail_len = n - t;
const Int tail_01 = tail_len * y_max;
const Int tail_11 = y_max * sum_range(t, n - 1);
const Int tail_02 = tail_len * y_max * y_max;
base = {head_01 + tail_01, head_11 + tail_11, head_02 + tail_02};
}
}
const Int si = sum_0_to_n_minus_1(n);
const Int si2 = sum_0_to_n_minus_1_sq(n);
Result<Int> ans;
ans.ans_01 = qa * si + qb * n + base.ans_01;
ans.ans_11 = qa * si2 + qb * si + base.ans_11;
ans.ans_02 = qa * qa * si2 + 2 * qa * qb * si + 2 * qa * base.ans_11 +
qb * qb * n + 2 * qb * base.ans_01 + base.ans_02;
return ans;
}
} // namespace generalized_floor_sum_pq_le_2_internal
template <class T>
GeneralizedFloorSumPQLe2Result<T> generalized_floor_sum_pq_le_2(T n, T m, T a,
T b) {
static_assert(generalized_floor_sum_pq_le_2_internal::is_integral<T>::value,
"T must be integer.");
if constexpr (generalized_floor_sum_pq_le_2_internal::is_signed<T>::value)
assert(n >= 0);
assert(m > 0);
#ifdef __SIZEOF_INT128__
using I = __int128_t;
const auto res = generalized_floor_sum_pq_le_2_internal::solve<I>(
static_cast<I>(n), static_cast<I>(m), static_cast<I>(a),
static_cast<I>(b));
return {static_cast<T>(res.ans_01), static_cast<T>(res.ans_11),
static_cast<T>(res.ans_02)};
#else
const auto res =
generalized_floor_sum_pq_le_2_internal::solve<T>(n, m, a, b);
return {res.ans_01, res.ans_11, res.ans_02};
#endif
}
using i128 = __int128_t;
vector<FPS<mint>> matrixmul(vector<FPS<mint>> X, vector<FPS<mint>> Y) {
vector<FPS<mint>> Z(4);
Z = {
X[0] * Y[0] + X[1] * Y[2],
X[0] * Y[1] + X[1] * Y[3],
X[2] * Y[0] + X[3] * Y[2],
X[2] * Y[1] + X[3] * Y[3]
};
return Z;
}
ll op(ll a, ll b){
return a + b;
}
ll e(){
return 0;
}
ll mapping(ll a, ll b){
return (a == inf ? b : a);
}
ll composition(ll a, ll b){
return (a == inf ? b : a);
}
ll id(){
return inf;
}
struct ss{
long long value;
int size;
};
ss op2(ss a, ss b){
return {a.value+b.value, a.size+b.size};
}
ss e2(){
return {0, 0};
}
ss mapping2(ll a, ss b){
if(a != inf) b.value = a*b.size;
return b;
}
ll composition2(ll a, ll b){
return (a == inf ? b : a);
}
ll id2(){
return inf;
}
clock_t st;
void beg(ll ep, ll mo, bool nc, bool fac){
st = clock();
mod = mo;
ios::sync_with_stdio(false);
std::cin.tie(nullptr);
cout << fixed << setprecision(20);
if(nc)init();//二項係数 階乗(fact[])
srand((unsigned int)time(NULL));
if(fac)prepare_factorize();//素因数分解
rep(i, ep){
eps /= 10;
}
}
ll kp = 0;
bool ff(ll x){
if(x >= kp){
return true;
}
else{
return false;
}
}
std::random_device rd;
std::mt19937_64 mt(rd());
void nowtime(){
cout << ((double)(clock()) - (double)(st)) / CLOCKS_PER_SEC << endl;
}
double nowtimed(){
return ((double)(clock()) - (double)(st)) / CLOCKS_PER_SEC;
}
ll bits_msb(ll v )
{
v = v | (v >> 1);
v = v | (v >> 2);
v = v | (v >> 4);
v = v | (v >> 8);
v = v | (v >> 16);
v = v | (v >> 32);
return v ^ (v >> 1);
}
ll ssqr(ll a){
ll ok = 0, ng = 2000000000;
while(ng - ok > 1){
ll mi = (ok + ng) / 2;
if(mi * mi <= a){
ok = mi;
}
else{
ng = mi;
}
}
return ok;
}
void solve(ll P){
vl A(P - 1);
ll x;
rep(i, P - 1){
cout << '?' << ' ' << i + 1 << ' ' << i + 1 << endl;
cin >> A[i];
A[i]--;
}
cout << "? 1 " << P << endl;
cin >> x;
x--;
vl B(P), C(P);
vb ch(P, false);
if(x % P == A[0] % P){
rep(i, P - 1){
B[i] = A[i] % P;
ch[A[i] % P] = true;
C[i] = A[i] / P;
}
C[P - 1] = x / P;
rep(i, P){
if(!ch[i]){
B[P - 1] = i;
}
}
cout << '!' << endl;
rep(i, P){
rep(j, P){
cout << B[i] + C[j] * P + 1 << ' ';
}
cout << endl;
}
}
else{
rep(i, P - 1){
B[i] = A[i] / P;
ch[A[i] / P] = true;
C[i] = A[i] % P;
}
C[P - 1] = x % P;
rep(i, P){
if(!ch[i]){
B[P - 1] = i;
}
}
cout << '!' << endl;
rep(i, P){
rep(j, P){
cout << C[j] + B[i] * P + 1 << ' ';
}
cout << endl;
}
}
return ;
}
int main()
{
beg(12, 998244353, false, false);// eps mod nck factorize max変更忘れない！ define外せ！
ll T;
T = 1;
//cin >> T;
while(T--){
ll P;
cin >> P;
solve(P);
}
}