結果
| 問題 |
No.2556 Increasing Matrix
|
| コンテスト | |
| ユーザー |
 maroon_kuri
|
| 提出日時 | 2023-12-17 18:22:49 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 265 ms / 6,000 ms |
| コード長 | 35,281 bytes |
| コンパイル時間 | 5,138 ms |
| コンパイル使用メモリ | 274,844 KB |
| 最終ジャッジ日時 | 2025-02-18 11:57:15 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge1 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 22 |
ソースコード
#ifndef LOCAL
#pragma GCC optimize ("Ofast")
#pragma GCC optimize ("unroll-loops")
#endif
#include <bits/stdc++.h>
using namespace std;
using ll=long long;
#define int ll
#define rng(i,a,b) for(int i=int(a);i<int(b);i++)
#define rep(i,b) rng(i,0,b)
#define gnr(i,a,b) for(int i=int(b)-1;i>=int(a);i--)
#define per(i,b) gnr(i,0,b)
#define pb push_back
#define eb emplace_back
#define a first
#define b second
#define bg begin()
#define ed end()
#define all(x) x.bg,x.ed
#define si(x) int(x.size())
#ifdef LOCAL
#define dmp(x) cerr<<__LINE__<<" "<<#x<<" "<<x<<endl
#else
#define dmp(x) void(0)
#endif
template<class t,class u> bool chmax(t&a,u b){if(a<b){a=b;return true;}else return false;}
template<class t,class u> bool chmin(t&a,u b){if(b<a){a=b;return true;}else return false;}
template<class t> using vc=vector<t>;
template<class t> using vvc=vc<vc<t>>;
using pi=pair<int,int>;
using vi=vc<int>;
template<class t,class u>
ostream& operator<<(ostream& os,const pair<t,u>& p){
return os<<"{"<<p.a<<","<<p.b<<"}";
}
template<class t> ostream& operator<<(ostream& os,const vc<t>& v){
os<<"{";
for(auto e:v)os<<e<<",";
return os<<"}";
}
#define mp make_pair
#define mt make_tuple
#define one(x) memset(x,-1,sizeof(x))
#define zero(x) memset(x,0,sizeof(x))
#ifdef LOCAL
void dmpr(ostream&os){os<<endl;}
template<class T,class... Args>
void dmpr(ostream&os,const T&t,const Args&... args){
os<<t<<" ";
dmpr(os,args...);
}
#define dmp2(...) dmpr(cerr,__LINE__,##__VA_ARGS__)
#else
#define dmp2(...) void(0)
#endif
using uint=unsigned;
using ull=unsigned long long;
template<class t,size_t n>
ostream& operator<<(ostream&os,const array<t,n>&a){
return os<<vc<t>(all(a));
}
template<int i,class T>
void print_tuple(ostream&,const T&){
}
template<int i,class T,class H,class ...Args>
void print_tuple(ostream&os,const T&t){
if(i)os<<",";
os<<get<i>(t);
print_tuple<i+1,T,Args...>(os,t);
}
template<class ...Args>
ostream& operator<<(ostream&os,const tuple<Args...>&t){
os<<"{";
print_tuple<0,tuple<Args...>,Args...>(os,t);
return os<<"}";
}
ll read(){
ll i;
cin>>i;
return i;
}
vi readvi(int n,int off=0){
vi v(n);
rep(i,n)v[i]=read()+off;
return v;
}
pi readpi(int off=0){
int a,b;cin>>a>>b;
return pi(a+off,b+off);
}
template<class t>
void print_single(t x,int suc=1){
cout<<x;
if(suc==1)
cout<<"\n";
if(suc==2)
cout<<" ";
}
template<class t,class u>
void print_single(const pair<t,u>&p,int suc=1){
print_single(p.a,2);
print_single(p.b,suc);
}
template<class T>
void print_single(const vector<T>&v,int suc=1){
rep(i,v.size())
print_single(v[i],i==int(v.size())-1?suc:2);
}
template<class T>
void print_offset(const vector<T>&v,ll off,int suc=1){
rep(i,v.size())
print_single(v[i]+off,i==int(v.size())-1?suc:2);
}
template<class T,size_t N>
void print_single(const array<T,N>&v,int suc=1){
rep(i,N)
print_single(v[i],i==int(N)-1?suc:2);
}
template<class T>
void print(const T&t){
print_single(t);
}
template<class T,class ...Args>
void print(const T&t,const Args&...args){
print_single(t,2);
print(args...);
}
string readString(){
string s;
cin>>s;
return s;
}
template<class T>
T sq(const T& t){
return t*t;
}
void YES(bool ex=true){
cout<<"YES\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void NO(bool ex=true){
cout<<"NO\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void Yes(bool ex=true){
cout<<"Yes\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void No(bool ex=true){
cout<<"No\n";
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
//#define CAPITAL
/*
void yes(bool ex=true){
#ifdef CAPITAL
cout<<"YES"<<"\n";
#else
cout<<"Yes"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void no(bool ex=true){
#ifdef CAPITAL
cout<<"NO"<<"\n";
#else
cout<<"No"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}*/
void possible(bool ex=true){
#ifdef CAPITAL
cout<<"POSSIBLE"<<"\n";
#else
cout<<"Possible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
void impossible(bool ex=true){
#ifdef CAPITAL
cout<<"IMPOSSIBLE"<<"\n";
#else
cout<<"Impossible"<<"\n";
#endif
if(ex)exit(0);
#ifdef LOCAL
cout.flush();
#endif
}
constexpr ll ten(int n){
return n==0?1:ten(n-1)*10;
}
const ll infLL=LLONG_MAX/3;
#ifdef int
const int inf=infLL;
#else
const int inf=INT_MAX/2-100;
#endif
int topbit(signed t){
return t==0?-1:31-__builtin_clz(t);
}
int topbit(ll t){
return t==0?-1:63-__builtin_clzll(t);
}
int topbit(ull t){
return t==0?-1:63-__builtin_clzll(t);
}
int botbit(signed a){
return a==0?32:__builtin_ctz(a);
}
int botbit(ll a){
return a==0?64:__builtin_ctzll(a);
}
int botbit(ull a){
return a==0?64:__builtin_ctzll(a);
}
int popcount(signed t){
return __builtin_popcount(t);
}
int popcount(ll t){
return __builtin_popcountll(t);
}
int popcount(ull t){
return __builtin_popcountll(t);
}
int bitparity(ll t){
return __builtin_parityll(t);
}
bool ispow2(int i){
return i&&(i&-i)==i;
}
ll mask(int i){
return (ll(1)<<i)-1;
}
ull umask(int i){
return (ull(1)<<i)-1;
}
ll minp2(ll n){
if(n<=1)return 1;
else return ll(1)<<(topbit(n-1)+1);
}
bool inc(int a,int b,int c){
return a<=b&&b<=c;
}
template<class t> void mkuni(vc<t>&v){
sort(all(v));
v.erase(unique(all(v)),v.ed);
}
ll rand_int(ll l, ll r) { //[l, r]
//#ifdef LOCAL
static mt19937_64 gen;
/*#else
static mt19937_64 gen(chrono::steady_clock::now().time_since_epoch().count());
#endif*/
return uniform_int_distribution<ll>(l, r)(gen);
}
ll rand_int(ll k){ //[0,k)
return rand_int(0,k-1);
}
template<class t>
void myshuffle(vc<t>&a){
rep(i,si(a))swap(a[i],a[rand_int(0,i)]);
}
template<class t,class u>
int lwb(const vc<t>&v,const u&a){
return lower_bound(all(v),a)-v.bg;
}
template<class t,class u>
bool bis(const vc<t>&v,const u&a){
return binary_search(all(v),a);
}
vvc<int> readGraph(int n,int m){
vvc<int> g(n);
rep(i,m){
int a,b;
cin>>a>>b;
//sc.read(a,b);
a--;b--;
g[a].pb(b);
g[b].pb(a);
}
return g;
}
vvc<int> readTree(int n){
return readGraph(n,n-1);
}
template<class t>
vc<t> presum(const vc<t>&a){
vc<t> s(si(a)+1);
rep(i,si(a))s[i+1]=s[i]+a[i];
return s;
}
vc<ll> presum(const vi&a){
vc<ll> s(si(a)+1);
rep(i,si(a))s[i+1]=s[i]+a[i];
return s;
}
//BIT で数列を管理するときに使う (CF850C)
template<class t>
vc<t> predif(vc<t> a){
gnr(i,1,si(a))a[i]-=a[i-1];
return a;
}
template<class t>
vvc<ll> imos(const vvc<t>&a){
int n=si(a),m=si(a[0]);
vvc<ll> b(n+1,vc<ll>(m+1));
rep(i,n)rep(j,m)
b[i+1][j+1]=b[i+1][j]+b[i][j+1]-b[i][j]+a[i][j];
return b;
}
//verify してないや
void transvvc(int&n,int&m){
swap(n,m);
}
template<class t,class... Args>
void transvvc(int&n,int&m,vvc<t>&a,Args&...args){
assert(si(a)==n);
vvc<t> b(m,vi(n));
rep(i,n){
assert(si(a[i])==m);
rep(j,m)b[j][i]=a[i][j];
}
a.swap(b);
transvvc(n,m,args...);
}
//CF854E
void rotvvc(int&n,int&m){
swap(n,m);
}
template<class t,class... Args>
void rotvvc(int&n,int&m,vvc<t>&a,Args&...args){
assert(si(a)==n);
vvc<t> b(m,vi(n));
rep(i,n){
assert(si(a[i])==m);
rep(j,m)b[m-1-j][i]=a[i][j];
}
a.swap(b);
rotvvc(n,m,args...);
}
//ソートして i 番目が idx[i]
//CF850C
template<class t>
vi sortidx(const vc<t>&a){
int n=si(a);
vi idx(n);iota(all(idx),0);
sort(all(idx),[&](int i,int j){return a[i]<a[j];});
return idx;
}
//vs[i]=a[idx[i]]
//例えば sortidx で得た idx を使えば単にソート列になって返ってくる
//CF850C
template<class t>
vc<t> a_idx(const vc<t>&a,const vi&idx){
int n=si(a);
assert(si(idx)==n);
vc<t> vs(n);
rep(i,n)vs[i]=a[idx[i]];
return vs;
}
//CF850C
vi invperm(const vi&p){
int n=si(p);
vi q(n);
rep(i,n)q[p[i]]=i;
return q;
}
template<class t,class s=t>
s SUM(const vc<t>&a){
return accumulate(all(a),s(0));
}
template<class t>
t MAX(const vc<t>&a){
return *max_element(all(a));
}
template<class t>
pair<t,int> MAXi(const vc<t>&a){
auto itr=max_element(all(a));
return mp(*itr,itr-a.bg);
}
template<class t>
t MIN(const vc<t>&a){
return *min_element(all(a));
}
template<class t>
pair<t,int> MINi(const vc<t>&a){
auto itr=min_element(all(a));
return mp(*itr,itr-a.bg);
}
vi vid(int n){
vi res(n);iota(all(res),0);
return res;
}
template<class S>
void soin(S&s){
sort(all(s));
}
template<class S,class F>
void soin(S&s,F&&f){
sort(all(s),forward<F>(f));
}
template<class S>
S soout(S s){
soin(s);
return s;
}
template<class S>
void rein(S&s){
reverse(all(s));
}
template<class S>
S reout(S s){
rein(s);
return s;
}
template<class t,class u>
pair<t,u>&operator+=(pair<t,u>&a,pair<t,u> b){
a.a+=b.a;a.b+=b.b;return a;}
template<class t,class u>
pair<t,u>&operator-=(pair<t,u>&a,pair<t,u> b){
a.a-=b.a;a.b-=b.b;return a;}
template<class t,class u>
pair<t,u> operator+(pair<t,u> a,pair<t,u> b){return mp(a.a+b.a,a.b+b.b);}
template<class t,class u>
pair<t,u> operator-(pair<t,u> a,pair<t,u> b){return mp(a.a-b.a,a.b-b.b);}
template<class t>
t gpp(vc<t>&vs){
assert(si(vs));
t res=move(vs.back());
vs.pop_back();
return res;
}
template<class t,class u>
void pb(vc<t>&a,const vc<u>&b){
a.insert(a.ed,all(b));
}
template<class t,class...Args>
vc<t> cat(vc<t> a,Args&&...b){
(pb(a,forward<Args>(b)),...);
return a;
}
template<class t,class u>
vc<t>& operator+=(vc<t>&a,u x){
for(auto&v:a)v+=x;
return a;
}
template<class t,class u>
vc<t> operator+(vc<t> a,u x){
return a+=x;
}
template<class t,class u>
vc<t>& operator-=(vc<t>&a,u x){
for(auto&v:a)v-=x;
return a;
}
template<class t,class u>
vc<t>& operator-(vc<t> a,u x){
return a-=x;
}
template<class t,class u>
void remval(vc<t>&a,const u&v){
a.erase(remove(all(a),v),a.ed);
}
template<class t,class u>
void fila(vc<t>&vs,const u&a){
fill(all(vs),a);
}
template<class t,class u>
int findid(const vc<t>&vs,const u&a){
auto itr=find(all(vs),a);
if(itr==vs.ed)return -1;
else return itr-vs.bg;
}
template<class t>
void rtt(vc<t>&vs,int i){
rotate(vs.bg,vs.bg+i,vs.ed);
}
//mint107 は verify してねえ
//#define DYNAMIC_MOD
struct modinfo{uint mod,root;
#ifdef DYNAMIC_MOD
constexpr modinfo(uint m,uint r):mod(m),root(r),im(0){set_mod(m);}
ull im;
constexpr void set_mod(uint m){
mod=m;
im=ull(-1)/m+1;
}
uint product(uint a,uint b)const{
ull z=ull(a)*b;
uint x=((unsigned __int128)z*im)>>64;
uint v=uint(z)-x*mod;
return v<mod?v:v+mod;
}
#endif
};
template<modinfo const&ref>
struct modular{
static constexpr uint const &mod=ref.mod;
static modular root(){return modular(ref.root);}
uint v;
//modular(initializer_list<uint>ls):v(*ls.bg){}
modular(ll vv=0){s(vv%mod+mod);}
modular& s(uint vv){
v=vv<mod?vv:vv-mod;
return *this;
}
modular operator-()const{return modular()-*this;}
modular& operator+=(const modular&rhs){return s(v+rhs.v);}
modular&operator-=(const modular&rhs){return s(v+mod-rhs.v);}
modular&operator*=(const modular&rhs){
#ifndef DYNAMIC_MOD
v=ull(v)*rhs.v%mod;
#else
v=ref.product(v,rhs.v);
#endif
return *this;
}
modular&operator/=(const modular&rhs){return *this*=rhs.inv();}
modular operator+(const modular&rhs)const{return modular(*this)+=rhs;}
modular operator-(const modular&rhs)const{return modular(*this)-=rhs;}
modular operator*(const modular&rhs)const{return modular(*this)*=rhs;}
modular operator/(const modular&rhs)const{return modular(*this)/=rhs;}
modular pow(ll n)const{
if(n<0)return inv().pow(-n);
modular res(1),x(*this);
while(n){
if(n&1)res*=x;
x*=x;
n>>=1;
}
return res;
}
modular inv()const{return pow(mod-2);}
/*modular inv()const{
int x,y;
int g=extgcd<ll>(v,mod,x,y);
assert(g==1);
if(x<0)x+=mod;
return modular(x);
}*/
friend modular operator+(ll x,const modular&y){
return modular(x)+y;
}
friend modular operator-(ll x,const modular&y){
return modular(x)-y;
}
friend modular operator*(ll x,const modular&y){
return modular(x)*y;
}
friend modular operator/(ll x,const modular&y){
return modular(x)/y;
}
friend ostream& operator<<(ostream&os,const modular&m){
return os<<m.v;
}
friend istream& operator>>(istream&is,modular&m){
ll x;is>>x;
m=modular(x);
return is;
}
bool operator<(const modular&r)const{return v<r.v;}
bool operator==(const modular&r)const{return v==r.v;}
bool operator!=(const modular&r)const{return v!=r.v;}
explicit operator bool()const{
return v;
}
};
#define USE_GOOD_MOD
//size of input must be a power of 2
//output of forward fmt is bit-reversed
//output elements are in the range [0,mod*4)
//input of inverse fmt should be bit-reversed
template<class mint>
void inplace_fmt(const int n,mint*const f,bool inv){
static constexpr uint mod=mint::mod;
static constexpr uint mod2=mod*2;
static constexpr int L=30;
static mint g[L],ig[L],p2[L];
if(g[0].v==0){
rep(i,L){
mint w=-mint::root().pow(((mod-1)>>(i+2))*3);
g[i]=w;
ig[i]=w.inv();
p2[i]=mint(1<<i).inv();
}
}
if(!inv){
int b=n;
if(b>>=1){//input:[0,mod)
rep(i,b){
uint x=f[i+b].v;
f[i+b].v=f[i].v+mod-x;
f[i].v+=x;
}
}
if(b>>=1){//input:[0,mod*2)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
while(b){
if(b>>=1){//input:[0,mod*3)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
if(b>>=1){//input:[0,mod*4)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
}
}else{
int b=1;
if(b<n/2){//input:[0,mod)
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
ull x=f[j].v+mod-f[j+b].v;
f[j].v+=f[j+b].v;
f[j+b].v=x*p.v%mod;
}
p*=ig[__builtin_ctz(++k)];
}
b<<=1;
}
for(;b<n/2;b<<=1){
mint p=1;
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b/2){//input:[0,mod*2)
ull x=f[j].v+mod2-f[j+b].v;
f[j].v+=f[j+b].v;
f[j].v=(f[j].v)<mod2?f[j].v:f[j].v-mod2;
f[j+b].v=x*p.v%mod;
}
rng(j,i+b/2,i+b){//input:[0,mod)
ull x=f[j].v+mod-f[j+b].v;
f[j].v+=f[j+b].v;
f[j+b].v=x*p.v%mod;
}
p*=ig[__builtin_ctz(++k)];
}
}
if(b<n){//input:[0,mod*2)
rep(i,b){
uint x=f[i+b].v;
f[i+b].v=f[i].v+mod2-x;
f[i].v+=x;
}
}
mint z=p2[__lg(n)];
rep(i,n)f[i]*=z;
}
}
template<class mint>
void inplace_fmt(vector<mint>&f,bool inv){
inplace_fmt(si(f),f.data(),inv);
}
//size of input must be a power of 2
//output elements are in the range [0,mod*4)
template<class mint>
void half_fmt(const int n,mint*const f){
static constexpr uint mod=mint::mod;
static constexpr uint mod2=mod*2;
static const int L=30;
static mint g[L],h[L];
if(g[0].v==0){
rep(i,L){
g[i]=-mint::root().pow(((mod-1)>>(i+2))*3);
h[i]=mint::root().pow((mod-1)>>(i+2));
}
}
int b=n;
int lv=0;
if(b>>=1){//input:[0,mod)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
if(b>>=1){//input:[0,mod*2)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
while(b){
if(b>>=1){//input:[0,mod*3)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
if(b>>=1){//input:[0,mod*4)
mint p=h[lv++];
for(int i=0,k=0;i<n;i+=b*2){
rng(j,i,i+b){
uint x=(f[j+b]*p).v;
f[j].v=(f[j].v<mod2?f[j].v:f[j].v-mod2);
f[j+b].v=f[j].v+mod-x;
f[j].v+=x;
}
p*=g[__builtin_ctz(++k)];
}
}
}
}
template<class mint>
void half_fmt(vector<mint>&f){
half_fmt(si(f),f.data());
}
#ifdef USE_GOOD_MOD
template<class mint>
vc<mint> multiply(vc<mint> x,const vc<mint>&y,bool same=false){
int n=si(x)+si(y)-1;
int s=1;
while(s<n)s*=2;
x.resize(s);inplace_fmt(x,false);
if(!same){
static vc<mint> z;
z.clear();z.resize(s);
rep(i,si(y))z[i]=y[i];
inplace_fmt(z,false);
rep(i,s)x[i]*=z[i];
}else{
rep(i,s)x[i]*=x[i];
}
inplace_fmt(x,true);x.resize(n);
return x;
}
template<class mint>
vc<mint> multiply_givenlength(vc<mint> x,const vc<mint>&y,bool same=false){
int s=si(x);
assert(ispow2(s));
assert(si(y));
x.resize(s);inplace_fmt(x,false);
if(!same){
static vc<mint> z;
z.clear();z.resize(s);
rep(i,si(y))z[i]=y[i];
inplace_fmt(z,false);
rep(i,s)x[i]*=z[i];
}else{
rep(i,s)x[i]*=x[i];
}
inplace_fmt(x,true);
return x;
}
#else
//59501818244292734739283969-1=5.95*10^25 までの値を正しく計算
//最終的な列の大きさが 2^24 までなら動く
//最終的な列の大きさが 2^20 以下のときは，下の 3 つの素数を使ったほうが速い（は？）
//VERIFY: yosupo
//Yukicoder No980 (same=true)
namespace arbitrary_convolution{
constexpr modinfo base0{167772161,3};//2^25 * 5 + 1
constexpr modinfo base1{469762049,3};//2^26 * 7 + 1
constexpr modinfo base2{754974721,11};//2^24 * 45 + 1
//extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
//extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
//extern constexpr modinfo base2{1053818881,7};//2^20 * 1005 + 1
using mint0=modular<base0>;
using mint1=modular<base1>;
using mint2=modular<base2>;
template<class t,class mint>
vc<t> sub(const vc<mint>&x,const vc<mint>&y,bool same=false){
int n=si(x)+si(y)-1;
int s=1;
while(s<n)s*=2;
vc<t> z(s);rep(i,si(x))z[i]=x[i].v;
inplace_fmt(z,false);
if(!same){
vc<t> w(s);rep(i,si(y))w[i]=y[i].v;
inplace_fmt(w,false);
rep(i,s)z[i]*=w[i];
}else{
rep(i,s)z[i]*=z[i];
}
inplace_fmt(z,true);z.resize(n);
return z;
}
template<class mint>
vc<mint> multiply(const vc<mint>&x,const vc<mint>&y,bool same=false){
auto d0=sub<mint0>(x,y,same);
auto d1=sub<mint1>(x,y,same);
auto d2=sub<mint2>(x,y,same);
int n=si(d0);
vc<mint> res(n);
static const mint1 r01=mint1(mint0::mod).inv();
static const mint2 r02=mint2(mint0::mod).inv();
static const mint2 r12=mint2(mint1::mod).inv();
static const mint2 r02r12=r02*r12;
static const mint w1=mint(mint0::mod);
static const mint w2=w1*mint(mint1::mod);
rep(i,n){
ull a=d0[i].v;
ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
res[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
}
return res;
}
template<class t,class mint>
vc<t>&sub_givenlength(const vc<mint>&x,const vc<mint>&y,bool same=false){
int s=si(x);
assert(ispow2(s));
assert(si(y)==s);
static vc<t> z;
z.clear();z.resize(s);
rep(i,si(x))z[i]=x[i].v;
inplace_fmt(z,false);
if(!same){
static vc<t> w;
w.clear();w.resize(s);
rep(i,si(y))w[i]=y[i].v;
inplace_fmt(w,false);
rep(i,s)z[i]*=w[i];
}else{
rep(i,s)z[i]*=z[i];
}
inplace_fmt(z,true);
return z;
}
template<class mint>
vc<mint> multiply_givenlength(vc<mint> x,const vc<mint>&y,bool same=false){
auto&d0=sub_givenlength<mint0>(x,y,same);
auto&d1=sub_givenlength<mint1>(x,y,same);
auto&d2=sub_givenlength<mint2>(x,y,same);
int n=si(d0);
x.resize(n);
static const mint1 r01=mint1(mint0::mod).inv();
static const mint2 r02=mint2(mint0::mod).inv();
static const mint2 r12=mint2(mint1::mod).inv();
static const mint2 r02r12=r02*r12;
static const mint w1=mint(mint0::mod);
static const mint w2=w1*mint(mint1::mod);
rep(i,n){
ull a=d0[i].v;
ull b=(d1[i].v+mint1::mod-a)*r01.v%mint1::mod;
ull c=((d2[i].v+mint2::mod-a)*r02r12.v+(mint2::mod-b)*r12.v)%mint2::mod;
x[i].v=(a+b*w1.v+c*w2.v)%mint::mod;
}
return x;
}
}
using arbitrary_convolution::multiply;
using arbitrary_convolution::multiply_givenlength;
#endif
//UTPC2021 C
namespace integer_convolution{
extern constexpr modinfo base0{1045430273,3};//2^20 * 997 + 1
extern constexpr modinfo base1{1051721729,6};//2^20 * 1003 + 1
//extern constexpr modinfo base0{469762049,3};//2^26 * 7 + 1
//extern constexpr modinfo base1{754974721,11};//2^24 * 45 + 1
using mint0=modular<base0>;
using mint1=modular<base1>;
template<class t>
vc<t> sub(const vi&x,const vi&y,bool same=false){
int n=si(x)+si(y)-1;
int s=1;
while(s<n)s*=2;
vc<t> z(s);rep(i,si(x))z[i]=x[i];
inplace_fmt(z,false);
if(!same){
vc<t> w(s);rep(i,si(y))w[i]=y[i];
inplace_fmt(w,false);
rep(i,s)z[i]*=w[i];
}else{
rep(i,s)z[i]*=z[i];
}
inplace_fmt(z,true);z.resize(n);
return z;
}
vi multiply(const vi&x,const vi&y,bool same=false){
auto d0=sub<mint0>(x,y,same);
auto d1=sub<mint1>(x,y,same);
const mint1 r=mint1(mint0::mod).inv();
const ll v=ll(mint0::mod)*mint1::mod;
int n=si(d0);
vi res(n);
rep(i,n){
res[i]=d0[i].v+(r*(d1[i]-d0[i].v)).v*(ull)mint0::mod;
if(res[i]>v/2)res[i]-=v;
}
return res;
}
}
//最大で 1<<mx のサイズの fft が登場！
template<class mint>
vc<mint> large_convolution(const vc<mint>&a,const vc<mint>&b,int mx){
int n=si(a),m=si(b);
vc<mint> c(n+m-1);
int len=1<<(mx-1);
for(int i=0;i<n;i+=len){
for(int j=0;j<n;j+=len){
int x=min(len,n-i),y=min(len,m-j);
auto d=multiply(vc<mint>(a.bg+i,a.bg+i+x),vc<mint>(b.bg+j,b.bg+j+y));
rep(k,si(d))
c[i+j+k]+=d[k];
}
}
return c;
}
//input A: N 次,B ?,M
//output D: M 次多項式
//C を M 次多項式として
//[x^N] A*B*C = [x^M] D*C
//となるような D を返す
//CF796F
template<class mint>
vc<mint> transpose_advance(const vc<mint>&a,const vc<mint>&b,int m){
int n=si(a)-1;
auto d=multiply(a,b);
vc<mint> res(m+1);
if(n>=m){
rep(i,m+1)res[i]=d[i+n-m];
}else{
rng(i,m-n,m+1)res[i]=d[i+n-m];
}
return res;
}
//Yukicoder 2166
template<class mint>
void chmult(vc<mint>&x,const vc<mint>&y,int s){
x=multiply(move(x),y);
x.resize(s);
}
//Poly というのは常にサイズ 1 以上であることにしよう
//low のあたりをかならずサイズ s のものを返すようにいじった
//その影響で何かが起きているかも知れないし，起きていないかも知れない
template<class mint>
struct Poly:public vc<mint>{
/*Poly(){}
//Poly(const vc<mint>&val):vc<mint>(val){}
//Poly(vc<mint>&&val):vc<mint>(val){}
explicit Poly(int n):vc<mint>(n){}
explicit Poly(int n,mint v):vc<mint>(n,v){}
//Poly(initializer_list<mint>init):vc<mint>(all(init)){}
template<class...Args>
Poly(Args&&...args):vc<mint>(forward<Args>(args)...){}*/
using vc<mint>::vector;
using vc<mint>::operator=;
//Poly(const Poly<mint>&rhs):vc<mint>((vc<mint>)rhs){}
//Poly(Poly<mint>&&rhs):vc<mint>(forward<vc<mint>>(rhs)){}
int size()const{
return vc<mint>::size();
}
void ups(int s){
if(size()<s)this->resize(s,0);
}
Poly low(int s)const{
assert(s);
Poly res(s);
rep(i,min(s,size()))res[i]=(*this)[i];
return res;
}
Poly rev()const{
auto r=*this;
reverse(all(r));
return r;
}
Poly operator>>(int x)const{
assert(x<size());
Poly res(size()-x);
rep(i,size()-x)res[i]=(*this)[i+x];
return res;
}
Poly operator<<(int x)const{
Poly res(size()+x);
rep(i,size())res[i+x]=(*this)[i];
return res;
}
mint freq(int i)const{
return i<size()?(*this)[i]:0;
}
Poly operator-()const{
Poly res=*this;
for(auto&v:res)v=-v;
return res;
}
Poly& operator+=(const Poly&r){
ups(r.size());
rep(i,r.size())
(*this)[i]+=r[i];
return *this;
}
template<class T>
Poly& operator+=(T t){
(*this)[0]+=t;
return *this;
}
Poly& operator-=(const Poly&r){
ups(r.size());
rep(i,r.size())
(*this)[i]-=r[i];
return *this;
}
template<class T>
Poly& operator-=(T t){
(*this)[0]-=t;
return *this;
}
template<class T>
Poly& operator*=(T t){
for(auto&v:*this)
v*=t;
return *this;
}
Poly& operator*=(const Poly&r){
*this=multiply(*this,r);;
return *this;
}
Poly square()const{
return multiply(*this,*this,true);
}
#ifndef USE_GOOD_MOD
Poly inv(int s)const{
Poly r{mint(1)/(*this)[0]};
for(int n=1;n<s;n*=2)
r=r*2-(r.square()*low(2*n)).low(2*n);
r.resize(s);
return r;
}
#else
//source: Section 4 of "Removing redundancy from high-precision Newton iteration"
// 5/3
Poly inv(int s)const{
Poly r(s);
r[0]=mint(1)/(*this)[0];
for(int n=1;n<s;n*=2){
vc<mint> f=low(2*n);
f.resize(2*n);
inplace_fmt(f,false);
vc<mint> g=r.low(2*n);
g.resize(2*n);
inplace_fmt(g,false);
rep(i,2*n)f[i]*=g[i];
inplace_fmt(f,true);
rep(i,n)f[i]=0;
inplace_fmt(f,false);
rep(i,2*n)f[i]*=g[i];
inplace_fmt(f,true);
rng(i,n,min(2*n,s))r[i]=-f[i];
}
return r;
}
#endif
template<class T>
Poly& operator/=(T t){
return *this*=mint(1)/mint(t);
}
Poly quotient(const Poly&r,const Poly&rri)const{
int m=r.size();
assert(r[m-1].v);
int n=size();
int s=n-m+1;
if(s<=0) return {0};
return (rev().low(s)*rri.low(s)).low(s).rev();
}
Poly& operator/=(const Poly&r){
return *this=quotient(r,r.rev().inv(max(size()-r.size(),int(0))+1));
}
Poly& operator%=(const Poly&r){
*this-=*this/r*r;
return *this=low(r.size()-1);
}
Poly operator+(const Poly&r)const{return Poly(*this)+=r;}
template<class T>
Poly operator+(T t)const{return Poly(*this)+=t;}
template<class T>
friend Poly operator+(T t,Poly r){
r[0]+=t;
return r;
}
Poly operator-(const Poly&r)const{return Poly(*this)-=r;}
template<class T>
Poly operator-(T t)const{return Poly(*this)-=t;}
template<class T>
friend Poly operator-(T t,Poly r){
for(auto&v:r)v=-v;
r[0]+=t;
return r;
}
template<class T>
Poly operator*(T t)const{return Poly(*this)*=t;}
Poly operator*(const Poly&r)const{return Poly(*this)*=r;}
template<class T>
Poly operator/(T t)const{return Poly(*this)/=t;}
Poly operator/(const Poly&r)const{return Poly(*this)/=r;}
Poly operator%(const Poly&r)const{return Poly(*this)%=r;}
Poly dif()const{
assert(size());
if(size()==1){
return {0};
}else{
Poly r(size()-1);
rep(i,r.size())
r[i]=(*this)[i+1]*(i+1);
return r;
}
}
Poly inte(const mint invs[])const{
Poly r(size()+1,0);
rep(i,size())
r[i+1]=(*this)[i]*invs[i+1];
return r;
}
//VERIFY: yosupo
//opencupXIII GP of Peterhof H
Poly log(int s,const mint invs[])const{
assert((*this)[0]==1);
if(s==1)return {0};
return (low(s).dif()*inv(s-1)).low(s-1).inte(invs);
}
//Petrozavodsk 2019w mintay1 G
//yosupo judge
//UOJ Round23 C
Poly exp(int s,const mint invs[])const{
assert((*this)[0]==mint(0));
Poly f{1},g{1};
for(int n=1;;n*=2){
if(n>=s)break;
g=g*2-(g.square()*f).low(n);
//if(n>=s)break;
Poly q=low(n).dif();
q=q+g*(f.dif()-f*q).low(2*n-1);
f=f+(f*(low(2*n)-q.inte(invs))).low(2*n);
}
return f.low(s);
}
//exp(x),exp(-x) のペアを返す
//UOJ Round23 C
pair<Poly,Poly> exp2(int s,const mint invs[])const{
assert((*this)[0]==mint(0));
Poly f{1},g{1};
for(int n=1;;n*=2){
//if(n>=s)break;
g=g*2-(g.square()*f).low(n);
if(n>=s)break;
Poly q=low(n).dif();
q=q+g*(f.dif()-f*q).low(2*n-1);
f=f+(f*(low(2*n)-q.inte(invs))).low(2*n);
}
return make_pair(f.low(s),g.low(s));
}
#ifndef USE_GOOD_MOD
//CF250 E
Poly sqrt(int s)const{
assert((*this)[0]==1);
static const mint half=mint(1)/mint(2);
Poly r{1};
for(int n=1;n<s;n*=2)
r=(r+(r.inv(n*2)*low(n*2)).low(n*2))*half;
return r.low(s);
}
#else
//11/6
//VERIFY: yosupo
Poly sqrt(int s)const{
assert((*this)[0]==1);
static const mint half=mint(1)/mint(2);
vc<mint> f{1},g{1},z{1};
for(int n=1;n<s;n*=2){
rep(i,n)z[i]*=z[i];
inplace_fmt(z,true);
vc<mint> delta(2*n);
rep(i,n)delta[n+i]=z[i]-freq(i)-freq(n+i);
inplace_fmt(delta,false);
vc<mint> gbuf(2*n);
rep(i,n)gbuf[i]=g[i];
inplace_fmt(gbuf,false);
rep(i,2*n)delta[i]*=gbuf[i];
inplace_fmt(delta,true);
f.resize(2*n);
rng(i,n,2*n)f[i]=-half*delta[i];
if(2*n>=s)break;
z=f;
inplace_fmt(z,false);
vc<mint> eps=gbuf;
rep(i,2*n)eps[i]*=z[i];
inplace_fmt(eps,true);
rep(i,n)eps[i]=0;
inplace_fmt(eps,false);
rep(i,2*n)eps[i]*=gbuf[i];
inplace_fmt(eps,true);
g.resize(2*n);
rng(i,n,2*n)g[i]=-eps[i];
}
f.resize(s);
return f;
}
#endif
pair<Poly,Poly> divide(const Poly&r,const Poly&rri)const{
Poly a=quotient(r,rri);
Poly b=*this-a*r;
return make_pair(a,b.low(r.size()-1));
}
//Yukicoder No.215
Poly pow_mod(int n,const Poly&r)const{
Poly rri=r.rev().inv(r.size());
Poly cur{1},x=*this%r;
while(n){
if(n%2)
cur=(cur*x).divide(r,rri).b;
x=(x*x).divide(r,rri).b;
n/=2;
}
return cur;
}
int lowzero()const{
rep(i,size())if((*this)[i]!=0)return i;
return size();
}
//VERIFY: yosupo
//UOJ Round23 C (z=0,p<0)
//Multiuni2023-4-B
Poly pow(int s,int p,const mint invs[])const{
assert(s>0);
if(p==0){
Poly res(s,0);
res[0]=1;
return res;
}
int n=size(),z=0;
for(;z<n&&(*this)[z]==0;z++);
assert(z==0||p>0);
if(z*p>=s)return Poly(s,0);
mint c=(*this)[z],cinv=c.inv();
mint d=c.pow(p);
int t=s-z*p;
Poly x(t);
rng(i,z,min(z+t,n))x[i-z]=(*this)[i]*cinv;
x=x.log(t,invs);
rep(i,t)x[i]*=p;
x=x.exp(t,invs);
rep(i,t)x[i]*=d;
Poly y(s);
rep(i,t)y[z*p+i]=x[i];
return y;
}
mint eval(mint x)const{
mint r=0,w=1;
for(auto v:*this){
r+=w*v;
w*=x;
}
return r;
}
};
//CF641 F2
//f*x^(-a)
template<class mint>
struct Laurent{
Poly<mint> f;
int a;
Laurent(const Poly<mint>&num,const Poly<mint>&den,int s){
a=den.lowzero();
assert(a<si(den));
f=(num*(den>>a).inv(s)).low(s);
}
Laurent(const Poly<mint>&ff,int aa):f(ff),a(aa){}
Laurent dif()const{
return Laurent(f*(-a)+(f.dif()<<1),a+1);
}
mint&operator[](int i){
assert(inc(0,i+a,si(f)-1));
return f[i+a];
}
};
template<class mint>
ll m2l(mint a){
return a.v<mint::mod/2?a.v:ll(a.v)-ll(mint::mod);
}
template<class mint>
void showpoly(const Poly<mint>&a){
vi tmp(si(a));
rep(i,si(a)){
tmp[i]=m2l(a[i]);
}
cerr<<tmp<<endl;
}
//source: Tellegen’s Principle into Practice
//Yukicoder No.1145
//top には，(x-a[i]) の積が入っている(a がサイズ s に拡張されていることに注意)
//なので例えば (1-a[i]x) の積が欲しい場合は，
// Poly<mint> f=s.top;
// Poly<mint> g(n+1);
// rep(i,n+1)g[i]=f[si(f)-1-i];
template<class mint>
struct subproduct_tree{
using poly=Poly<mint>;
int raws,s,h;
mint*buf;
vc<mint*>f;
vi len;
poly top;
void inner_product(const int n,const mint*a,const mint*b,mint*c){
rep(i,n)c[i]=a[i]*b[i];
}
//first n elements are fft-ed
//last n elements are raw data mod x^n-1
//the coefficient of x^n is v
//convert the whole array into size-2n fft-ed array
void doubling_fmt(const int n,mint*a,const mint v){
a[n]-=v*2;
half_fmt(n,a+n);
}
subproduct_tree(const vc<mint>&a){
raws=si(a);
s=1;while(s<si(a))s*=2;
h=__lg(s)+1;
buf=new mint[s*h*2];
f.resize(s*2);
len.resize(s*2);
{
mint*head=buf;
rng(i,1,s*2){
len[i]=s>>__lg(i);
f[i]=head;
head+=len[i]*2;
}
}
rep(i,s){
mint w=i<si(a)?a[i]:0;
f[s+i][0]=-w+1;
f[s+i][1]=-w-1;
}
if(s==1)f[1][1]=f[1][0];
gnr(i,1,s){
inner_product(len[i],f[i*2],f[i*2+1],f[i]);
copy(f[i],f[i]+len[i],f[i]+len[i]);
inplace_fmt(len[i],f[i]+len[i],true);
if(i>1)doubling_fmt(len[i],f[i],1);
}
top.resize(s+1);
rep(i,s)top[i]=f[1][s+i];
top[0]-=1;
top[s]=1;
}
~subproduct_tree(){
delete[] buf;
}
//VERIFY: yosupo
vc<mint> multieval(const poly&b){
mint*buf2=new mint[s*2];
vc<mint*> c(s*2);
{
mint*head=buf2;
rng(i,1,s*2){
if((i&(i-1))==0&&__lg(i)%2==0)head=buf2;
c[i]=head;
head+=len[i];
}
}
{
poly tmp=top.rev().inv(si(b)).rev()*b;
rep(i,s)c[1][i]=i<si(b)?tmp[si(b)-1+i]:0;
}
vc<mint> tmp(s);
rng(i,1,s){
inplace_fmt(len[i],c[i],false);
rep(k,2){
tmp.resize(len[i]);
rep(j,len[i])tmp[j]=f[i*2+(k^1)][j]*c[i][j];
inplace_fmt(tmp,true);
rep(j,len[i]/2)c[i*2+k][j]=tmp[len[i]/2+j];
}
}
vc<mint> ans(raws);
rep(i,raws)ans[i]=c[s+i][0];
delete[] buf2;
return ans;
}
poly interpolate(const vc<mint>&val){
mint*buf2=new mint[s*2*2];
vc<mint*> c(s*2);
{
mint*head=buf2;
rng(i,1,s*2){
if((i&(i-1))==0&&__lg(i)%2==0)head=buf2;
c[i]=head;
head+=len[i]*2;
}
}
{
vc<mint> z=multieval(poly(top.bg+(s-si(val)),top.ed).dif());
rep(i,s){
mint w=i<si(val)?val[i]/z[i]:0;
c[s+i][0]=c[s+i][1]=w;
}
}
gnr(i,1,s){
rep(j,len[i])
c[i][j]=c[i*2][j]*f[i*2+1][j]+c[i*2+1][j]*f[i*2][j];
copy(c[i],c[i]+len[i],c[i]+len[i]);
inplace_fmt(len[i],c[i]+len[i],true);
if(i>1)doubling_fmt(len[i],c[i],0);
}
poly res(c[1]+s+(s-si(val)),c[1]+s*2);
delete[] buf2;
return res;
}
//res[i]=prod_{j!=i} (a[i]-a[j])
//Yukicoder 2556
vc<mint> product_of_difference(){
return multieval(poly(top.bg+(s-raws),top.ed).dif());
}
};
#ifndef DYNAMIC_MOD
extern constexpr modinfo base{998244353,3};
//extern constexpr modinfo base{1000000007,0};
//extern constexpr modinfo base{2147483579,0};//2^31 未満の最大の安全素数
//modinfo base{1,0};
#ifdef USE_GOOD_MOD
static_assert(base.mod==998244353);
#endif
#else
modinfo base(1,0);
extern constexpr modinfo base107(1000000007,0);
using mint107=modular<base107>;
#endif
using mint=modular<base>;
mint parity(int i){
return i%2==0?1:-1;
}
#ifdef LOCAL
const int vmax=10010;
#else
const int vmax=(1<<21)+10;
#endif
mint fact[vmax],finv[vmax],invs[vmax];
void initfact(){
fact[0]=1;
rng(i,1,vmax){
fact[i]=fact[i-1]*i;
}
finv[vmax-1]=fact[vmax-1].inv();
for(int i=vmax-2;i>=0;i--){
finv[i]=finv[i+1]*(i+1);
}
for(int i=vmax-1;i>=1;i--){
invs[i]=finv[i]*fact[i-1];
}
}
mint choose(int n,int k){
return inc(0,k,n)?fact[n]*finv[n-k]*finv[k]:0;
}
mint binom(int a,int b){
return 0<=a&&0<=b?fact[a+b]*finv[a]*finv[b]:0;
}
mint catalan(int n){
return binom(n,n)-(n-1>=0?binom(n-1,n+1):0);
}
//対角線を超えず (x,y) に至る方法の数
mint catalan(int x,int y){
assert(y<=x);
return binom(x,y)-binom(x+1,y-1);
}
//y=x+c を超えず (x,y) に至る方法の数
mint catalan(int x,int y,int c){
assert(y<=x+c);
return binom(x,y)-binom(x+c+1,y-c-1);
}
/*
const int vmax=610;
mint fact[vmax+1],binbuf[vmax+1][vmax+1];
mint choose(int n,int k){
return 0<=k&&k<=n?binbuf[n-k][k]:0;
}
mint binom(int a,int b){
return 0<=a&&0<=b?binbuf[a][b]:0;
}
void initfact(int n){
fact[0]=1;
rep(i,n)fact[i+1]=fact[i]*(i+1);
rep(i,n+1)rep(j,n+1){
if(i==0&&j==0){
binbuf[i][j]=1;
}else{
binbuf[i][j]=0;
if(i)binbuf[i][j]+=binbuf[i-1][j];
if(j)binbuf[i][j]+=binbuf[i][j-1];
}
}
}
*/
mint p2[vmax],p2inv[vmax];
void initp2(){
p2[0]=1;
rep(i,vmax-1)p2[i+1]=p2[i]*2;
p2inv[vmax-1]=p2[vmax-1].inv();
per(i,vmax-1)p2inv[i]=p2inv[i+1]*2;
}
bool dbg=false;
void slv(){
int n;cin>>n;
vc<mint> a(n);
rep(i,n){
cin>>a[i];
a[i]+=i;
}
auto z=subproduct_tree(a).product_of_difference();
mint ans=1;
for(auto v:z)ans*=v;
ans*=parity(n*(n-1)/2);
rng(i,1,n)ans*=sq(finv[i]);
print(ans);
}
signed main(){
cin.tie(0);
ios::sync_with_stdio(0);
cout<<fixed<<setprecision(20);
initfact();
if(dbg){
while(1)slv();
}else{
//int t;cin>>t;rep(_,t)
slv();
}
}