結果
| 問題 |
No.2794 I Love EDPC-T
|
| コンテスト | |
| ユーザー |
 sigma425
|
| 提出日時 | 2024-07-01 07:19:05 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 82 ms / 3,000 ms |
| コード長 | 25,420 bytes |
| コンパイル時間 | 3,562 ms |
| コンパイル使用メモリ | 235,980 KB |
| 最終ジャッジ日時 | 2025-02-22 01:39:39 |
|
ジャッジサーバーID （参考情報） |
judge1 / judge3 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 3 |
| other | AC * 31 |
ソースコード
#line 1 "2794.cpp"
// #pragma GCC target("avx2,avx512f,avx512vl,avx512bw,avx512dq,avx512cd,avx512vbmi,avx512vbmi2,avx512vpopcntdq,avx512bitalg,bmi,bmi2,lzcnt,popcnt")
// #pragma GCC optimize("Ofast")
#line 2 "/home/sigma/comp/library/template.hpp"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using uint = unsigned int;
using ull = unsigned long long;
#define rep(i,n) for(int i=0;i<int(n);i++)
#define rep1(i,n) for(int i=1;i<=int(n);i++)
#define per(i,n) for(int i=int(n)-1;i>=0;i--)
#define per1(i,n) for(int i=int(n);i>0;i--)
#define all(c) c.begin(),c.end()
#define si(x) int(x.size())
#define pb push_back
#define eb emplace_back
#define fs first
#define sc second
template<class T> using V = vector<T>;
template<class T> using VV = vector<vector<T>>;
template<class T,class U> bool chmax(T& x, U y){
if(x<y){ x=y; return true; }
return false;
}
template<class T,class U> bool chmin(T& x, U y){
if(y<x){ x=y; return true; }
return false;
}
template<class T> void mkuni(V<T>& v){sort(all(v));v.erase(unique(all(v)),v.end());}
template<class T> int lwb(const V<T>& v, const T& a){return lower_bound(all(v),a) - v.begin();}
template<class T>
V<T> Vec(size_t a) {
return V<T>(a);
}
template<class T, class... Ts>
auto Vec(size_t a, Ts... ts) {
return V<decltype(Vec<T>(ts...))>(a, Vec<T>(ts...));
}
template<class S,class T> ostream& operator<<(ostream& o,const pair<S,T> &p){
return o<<"("<<p.fs<<","<<p.sc<<")";
}
template<class T> ostream& operator<<(ostream& o,const vector<T> &vc){
o<<"{";
for(const T& v:vc) o<<v<<",";
o<<"}";
return o;
}
constexpr ll TEN(int n) { return (n == 0) ? 1 : 10 * TEN(n-1); }
#ifdef LOCAL
#define show(x) cerr << "LINE" << __LINE__ << " : " << #x << " = " << (x) << endl
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 shows(...) cerr << "LINE" << __LINE__ << " : ";dmpr(cerr,##__VA_ARGS__)
#define dump(x) cerr << "LINE" << __LINE__ << " : " << #x << " = {"; \
for(auto v: x) cerr << v << ","; cerr << "}" << endl;
#else
#define show(x) void(0)
#define dump(x) void(0)
#define shows(...) void(0)
#endif
template<class D> D divFloor(D a, D b){
return a / b - (((a ^ b) < 0 && a % b != 0) ? 1 : 0);
}
template<class D> D divCeil(D a, D b) {
return a / b + (((a ^ b) > 0 && a % b != 0) ? 1 : 0);
}
/*
x 0 1 2 3 4 5 6 7 8 9
bsr(x) -1 0 1 1 2 2 2 2 3 3
最上位bit
*/
int bsr(int x){
return x == 0 ? -1 : 31 ^ __builtin_clz(x);
}
int bsr(uint x){
return x == 0 ? -1 : 31 ^ __builtin_clz(x);
}
int bsr(ll x){
return x == 0 ? -1 : 63 ^ __builtin_clzll(x);
}
int bsr(ull x){
return x == 0 ? -1 : 63 ^ __builtin_clzll(x);
}
/*
x 0 1 2 3 4 5 6 7 8 9
bsl(x) -1 0 1 0 2 0 1 0 3 0
最下位bit
*/
int bsl(int x){
if(x==0) return -1;
return __builtin_ctz(x);
}
int bsl(uint x){
if(x==0) return -1;
return __builtin_ctz(x);
}
int bsl(ll x){
if(x==0) return -1;
return __builtin_ctzll(x);
}
int bsl(ull x){
if(x==0) return -1;
return __builtin_ctzll(x);
}
template<class T>
T rnd(T l,T r){ //[l,r)
using D = uniform_int_distribution<T>;
static random_device rd;
static mt19937 gen(rd());
return D(l,r-1)(gen);
}
template<class T>
T rnd(T n){ //[0,n)
return rnd(T(0),n);
}
#line 1 "/home/sigma/comp/library/math/poly.cpp"
/*
2021/04/14 大幅変更
poly 基本, MultipointEval, Interpolate
*/
#line 1 "/home/sigma/comp/library/math/mint.cpp"
/*
任意mod なら
template なくして costexpr の行消して global に unsigned int mod = 1;
で cin>>mod してから使う
任意 mod はかなり遅いので、できれば "atcoder/modint" を使う
*/
template<unsigned int mod_>
struct ModInt{
using uint = unsigned int;
using ll = long long;
using ull = unsigned long long;
constexpr static uint mod = mod_;
uint v;
ModInt():v(0){}
ModInt(ll _v):v(normS(_v%mod+mod)){}
explicit operator bool() const {return v!=0;}
static uint normS(const uint &x){return (x<mod)?x:x-mod;} // [0 , 2*mod-1] -> [0 , mod-1]
static ModInt make(const uint &x){ModInt m; m.v=x; return m;}
ModInt operator+(const ModInt& b) const { return make(normS(v+b.v));}
ModInt operator-(const ModInt& b) const { return make(normS(v+mod-b.v));}
ModInt operator-() const { return make(normS(mod-v)); }
ModInt operator*(const ModInt& b) const { return make((ull)v*b.v%mod);}
ModInt operator/(const ModInt& b) const { return *this*b.inv();}
ModInt& operator+=(const ModInt& b){ return *this=*this+b;}
ModInt& operator-=(const ModInt& b){ return *this=*this-b;}
ModInt& operator*=(const ModInt& b){ return *this=*this*b;}
ModInt& operator/=(const ModInt& b){ return *this=*this/b;}
ModInt& operator++(int){ return *this=*this+1;}
ModInt& operator--(int){ return *this=*this-1;}
template<class T> friend ModInt operator+(T a, const ModInt& b){ return (ModInt(a) += b);}
template<class T> friend ModInt operator-(T a, const ModInt& b){ return (ModInt(a) -= b);}
template<class T> friend ModInt operator*(T a, const ModInt& b){ return (ModInt(a) *= b);}
template<class T> friend ModInt operator/(T a, const ModInt& b){ return (ModInt(a) /= b);}
ModInt pow(ll p) const {
if(p<0) return inv().pow(-p);
ModInt a = 1;
ModInt x = *this;
while(p){
if(p&1) a *= x;
x *= x;
p >>= 1;
}
return a;
}
ModInt inv() const { // should be prime
return pow(mod-2);
}
// ll extgcd(ll a,ll b,ll &x,ll &y) const{
// ll p[]={a,1,0},q[]={b,0,1};
// while(*q){
// ll t=*p/ *q;
// rep(i,3) swap(p[i]-=t*q[i],q[i]);
// }
// if(p[0]<0) rep(i,3) p[i]=-p[i];
// x=p[1],y=p[2];
// return p[0];
// }
// ModInt inv() const {
// ll x,y;
// extgcd(v,mod,x,y);
// return make(normS(x+mod));
// }
bool operator==(const ModInt& b) const { return v==b.v;}
bool operator!=(const ModInt& b) const { return v!=b.v;}
bool operator<(const ModInt& b) const { return v<b.v;}
friend istream& operator>>(istream &o,ModInt& x){
ll tmp;
o>>tmp;
x=ModInt(tmp);
return o;
}
friend ostream& operator<<(ostream &o,const ModInt& x){ return o<<x.v;}
// friend ostream& operator<<(ostream &o,const ModInt& x){
// for(int b=1;b<=100;b++){
// for(int a=-100;a<=100;a++){
// if(ModInt(a)/b == x){
// return o << a << "/" << b;
// }
// }
// }
// return o<<x.v;
// }
};
using mint = ModInt<998244353>;
//using mint = ModInt<1000000007>;
V<mint> fact,ifact,invs;
// a,b >= 0 のみ
mint Choose(int a,int b){
if(b<0 || a<b) return 0;
return fact[a] * ifact[b] * ifact[a-b];
}
/*
// b >= 0 の範囲で、 Choose(a,b) = a(a-1)..(a-b+1) / b!
mint Choose(int a,int b){
if(b<0 || a<b) return 0;
return fact[a] * ifact[b] * ifact[a-b];
}
*/
void InitFact(int N){ //[0,N]
N++;
fact.resize(N);
ifact.resize(N);
invs.resize(N);
fact[0] = 1;
rep1(i,N-1) fact[i] = fact[i-1] * i;
ifact[N-1] = fact[N-1].inv();
for(int i=N-2;i>=0;i--) ifact[i] = ifact[i+1] * (i+1);
rep1(i,N-1) invs[i] = fact[i-1] * ifact[i];
}
#line 7 "/home/sigma/comp/library/math/poly.cpp"
// inplace_fmt (without bit rearranging)
// fft:
// a[rev(i)] <- \sum_j \zeta^{ij} a[j]
// invfft:
// a[i] <- (1/n) \sum_j \zeta^{-ij} a[rev(j)]
// These two are inversions.
// !!! CHANGE IF MOD is unusual !!!
const int ORDER_2_MOD_MINUS_1 = 23; // ord_2 (mod-1)
const mint PRIMITIVE_ROOT = 3; // primitive root of (Z/pZ)*
void fft(V<mint>& a){
static constexpr uint mod = mint::mod;
static constexpr uint mod2 = mod + mod;
static const int H = ORDER_2_MOD_MINUS_1;
static const mint root = PRIMITIVE_ROOT;
static mint magic[H-1];
int n = si(a);
assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H); // n should be power of 2
if(!magic[0]){ // precalc
rep(i,H-1){
mint w = -root.pow(((mod-1)>>(i+2))*3);
magic[i] = w;
}
}
int m = n;
if(m >>= 1){
rep(i,m){
uint v = a[i+m].v; // < M
a[i+m].v = a[i].v + mod - v; // < 2M
a[i].v += v; // < 2M
}
}
if(m >>= 1){
mint p = 1;
for(int h=0,s=0; s<n; s += m*2){
for(int i=s;i<s+m;i++){
uint v = (a[i+m] * p).v; // < M
a[i+m].v = a[i].v + mod - v; // < 3M
a[i].v += v; // < 3M
}
p *= magic[__builtin_ctz(++h)];
}
}
while(m){
if(m >>= 1){
mint p = 1;
for(int h=0,s=0; s<n; s += m*2){
for(int i=s;i<s+m;i++){
uint v = (a[i+m] * p).v; // < M
a[i+m].v = a[i].v + mod - v; // < 4M
a[i].v += v; // < 4M
}
p *= magic[__builtin_ctz(++h)];
}
}
if(m >>= 1){
mint p = 1;
for(int h=0,s=0; s<n; s += m*2){
for(int i=s;i<s+m;i++){
uint v = (a[i+m] * p).v; // < M
a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v; // < 2M
a[i+m].v = a[i].v + mod - v; // < 3M
a[i].v += v; // < 3M
}
p *= magic[__builtin_ctz(++h)];
}
}
}
rep(i,n){
a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v; // < 2M
a[i].v = (a[i].v >= mod) ? a[i].v - mod : a[i].v; // < M
}
// finally < mod !!
}
void invfft(V<mint>& a){
static constexpr uint mod = mint::mod;
static constexpr uint mod2 = mod + mod;
static const int H = ORDER_2_MOD_MINUS_1;
static const mint root = PRIMITIVE_ROOT;
static mint magic[H-1];
int n = si(a);
assert(!(n & (n-1))); assert(n >= 1); assert(n <= 1<<H); // n should be power of 2
if(!magic[0]){ // precalc
rep(i,H-1){
mint w = -root.pow(((mod-1)>>(i+2))*3);
magic[i] = w.inv();
}
}
int m = 1;
if(m < n>>1){
mint p = 1;
for(int h=0,s=0; s<n; s += m*2){
for(int i=s;i<s+m;i++){
ull x = a[i].v + mod - a[i+m].v; // < 2M
a[i].v += a[i+m].v; // < 2M
a[i+m].v = (p.v * x) % mod; // < M
}
p *= magic[__builtin_ctz(++h)];
}
m <<= 1;
}
for(;m < n>>1; m <<= 1){
mint p = 1;
for(int h=0,s=0; s<n; s+= m*2){
for(int i=s;i<s+(m>>1);i++){
ull x = a[i].v + mod2 - a[i+m].v; // < 4M
a[i].v += a[i+m].v; // < 4M
a[i].v = (a[i].v >= mod2) ? a[i].v - mod2 : a[i].v; // < 2M
a[i+m].v = (p.v * x) % mod; // < M
}
for(int i=s+(m>>1); i<s+m; i++){
ull x = a[i].v + mod - a[i+m].v; // < 2M
a[i].v += a[i+m].v; // < 2M
a[i+m].v = (p.v * x) % mod; // < M
}
p *= magic[__builtin_ctz(++h)];
}
}
if(m < n){
rep(i,m){
uint x = a[i].v + mod2 - a[i+m].v; // < 4M
a[i].v += a[i+m].v; // < 4M
a[i+m].v = x; // < 4M
}
}
const mint in = mint(n).inv();
rep(i,n) a[i] *= in; // < M
// finally < mod !!
}
// A,B = 500000 -> 70ms
// verify https://judge.yosupo.jp/submission/44937
V<mint> multiply(V<mint> a, V<mint> b) {
int A = si(a), B = si(b);
if (!A || !B) return {};
int n = A+B-1;
int s = 1; while(s<n) s*=2;
if(a == b){ // # of fft call : 3 -> 2
a.resize(s); fft(a);
rep(i,s) a[i] *= a[i];
}else{
a.resize(s); fft(a);
b.resize(s); fft(b);
rep(i,s) a[i] *= b[i];
}
invfft(a); a.resize(n);
return a;
}
/*
係数アクセス
f[i] でいいが、 配列外参照する可能性があるなら at/set
*/
template<class mint>
struct Poly: public V<mint>{
using vector<mint>::vector;
Poly() {}
explicit Poly(int n) : V<mint>(n){} // poly<mint> a; a = 2; shouldn't be [0,0]
Poly(int n, mint c) : V<mint>(n,c){}
Poly(const V<mint>& a) : V<mint>(a){}
Poly(initializer_list<mint> li) : V<mint>(li){}
int size() const { return V<mint>::size(); }
mint at(int i) const {
return i<size() ? (*this)[i] : 0;
}
void set(int i, mint x){
if(i>=size() && !x) return;
while(i>=size()) this->pb(0);
(*this)[i] = x;
return;
}
mint operator()(mint x) const { // eval
mint res = 0;
int n = size();
mint a = 1;
rep(i,n){
res += a * (*this)[i];
a *= x;
}
return res;
}
Poly low(int n) const { // ignore x^n (take first n), but not empty
return Poly(this->begin(), this->begin()+min(max(n,1),size()));
}
Poly rev() const {
return Poly(this->rbegin(), this->rend());
}
friend ostream& operator<<(ostream &o,const Poly& f){
o << "[";
rep(i,f.size()){
o << f[i];
if(i != f.size()-1) o << ",";
}
o << "]";
return o;
}
Poly operator-() const {
Poly res = *this;
for(auto& v: res) v = -v;
return res;
}
Poly& operator+=(const mint& c){
if(this->empty()) this->eb(0);
(*this)[0] += c;
return *this;
}
Poly& operator-=(const mint& c){
if(this->empty()) this->eb(0);
(*this)[0] -= c;
return *this;
}
Poly& operator*=(const mint& c){
for(auto& v: *this) v *= c;
return *this;
}
Poly& operator/=(const mint& c){
return *this *= mint(1)/mint(c);
}
Poly& operator+=(const Poly& r){
if(size() < r.size()) this->resize(r.size(),0);
rep(i,r.size()) (*this)[i] += r[i];
return *this;
}
Poly& operator-=(const Poly& r){
if(size() < r.size()) this->resize(r.size(),0);
rep(i,r.size()) (*this)[i] -= r[i];
return *this;
}
Poly& operator*=(const Poly& r){
return *this = multiply(*this,r);
}
// 何回も同じrで割り算するなら毎回rinvを計算するのは無駄なので、呼び出し側で一回計算した後直接こっちを呼ぶと良い
// 取るべきinvの長さに注意
// 例えば mod r で色々計算したい時は、基本的に deg(r) * 2 長さの多項式を r で割ることになる
// とはいえいったん rinv を長く計算したらより短い場合はprefix見るだけだし、 rinv としてムダに長いものを渡しても問題ないので
// 割られる多項式として最大の次数を取ればよい
Poly quotient(const Poly& r, const Poly& rinv){
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)*rinv.low(s)).low(s).rev();
}
Poly& operator/=(const Poly& r){
return *this = quotient(r,r.rev().inv(max(size()-r.size(),0)+1));
}
Poly& operator%=(const Poly& r){
*this -= *this/r * r;
return *this = low(r.size()-1);
}
Poly operator+(const mint& c) const {return Poly(*this) += c; }
Poly operator-(const mint& c) const {return Poly(*this) -= c; }
Poly operator*(const mint& c) const {return Poly(*this) *= c; }
Poly operator/(const mint& c) const {return Poly(*this) /= c; }
Poly operator+(const Poly& r) const {return Poly(*this) += r; }
Poly operator-(const Poly& r) const {return Poly(*this) -= r; }
Poly operator*(const Poly& r) const {return Poly(*this) *= r; }
Poly operator/(const Poly& r) const {return Poly(*this) /= r; }
Poly operator%(const Poly& r) const {return Poly(*this) %= r; }
Poly diff() const {
Poly g(max(size()-1,0));
rep(i,g.size()) g[i] = (*this)[i+1] * (i+1);
return g;
}
Poly intg() const {
assert(si(invs) > size());
Poly g(size()+1);
rep(i,size()) g[i+1] = (*this)[i] * invs[i+1];
return g;
}
Poly square() const {
return multiply(*this,*this);
}
// 1/f(x) mod x^s
// N = s = 500000 -> 90ms
// inv は 5 回 fft(2n) を呼んでいるので、multiply が 3 回 fft(2n) を呼ぶのと比べると
// だいたい multiply の 5/3 倍の時間がかかる
// 導出: Newton
// fg = 1 mod x^m
// (fg-1)^2 = 0 mod x^2m
// f(2g-fg^2) = 1 mod x^2m
// verify: https://judge.yosupo.jp/submission/44938
Poly inv(int s) const {
Poly r(s);
r[0] = mint(1)/at(0);
for(int n=1;n<s;n*=2){ // 5 times fft : length 2n
V<mint> f = low(2*n); f.resize(2*n);
fft(f);
V<mint> g = r.low(2*n); g.resize(2*n);
fft(g);
rep(i,2*n) f[i] *= g[i];
invfft(f);
rep(i,n) f[i] = 0;
fft(f);
rep(i,2*n) f[i] *= g[i];
invfft(f);
for(int i=n;i<min(2*n,s);i++) r[i] -= f[i];
}
return r;
}
// log f mod x^s
// 導出: D log(f) = (D f) / f
// 500000: 180ms
// mult の 8/3 倍
// verify: https://judge.yosupo.jp/submission/44962
Poly log(int s) const {
assert(at(0) == 1);
if(s == 1) return {0};
return (low(s).diff() * inv(s-1)).low(s-1).intg();
}
// e^f mod x^s
// f.log(s).exp(s) == [1,0,...,0]
// 500000 : 440ms
// TODO: 高速化！
// 速い実装例 (hos): https://judge.yosupo.jp/submission/36732 150ms
// 導出 Newton:
// g = exp(f)
// log(g) - f = 0
// g == g0 mod x^m
// g == g0 - (log(g0) - f) / (1/g0) mod x^2m
// verify: yosupo
Poly exp(int s) const {
assert(at(0) == 0);
Poly f({1}),g({1});
for(int n=1;n<s;n*=2){
g = (g*2-g.square().low(n)*f).low(n);
Poly q = low(n).diff();
q = q + g * (f.diff() - f*q).low(2*n-1);
f = (f + f * (low(2*n)-q.intg()) ).low(2*n);
}
return f.low(s);
}
// f^p mod x^s
// 500000: 600ms
// 導出: f^p = e^(p log f)
// log 1回、 exp 1回
// Exp.cpp (Mifafa technique) も参照
// c.f. (f の non0 coef の個数) * s
// verify: https://judge.yosupo.jp/submission/44992
Poly pow(ll p, int s) const {
if(p == 0){
return Poly(s) + 1; // 0^0 is 1
}
int ord = 0;
while(ord<s && !at(ord)) ord++;
assert(!(p<0 and ord>0)); // 頑張ればできる
if(p>0 and (s-1)/p < ord) return Poly(s); // s <= p * ord
int off = p*ord;
int s_ = s-off;
const mint a0 = at(ord), ia0 = a0.inv(), ap = a0.pow(p);
Poly f(s_); rep(i,s_) f[i] = at(i+ord) * ia0;
f = (f.log(s_) * p).exp(s_);
Poly res(s);
rep(i,s_) res[i+off] = f[i] * ap;
return res;
}
// f^(1/2) mod x^s
// f[0] should be 1
// 11/6
// verify: https://judge.yosupo.jp/submission/44997
Poly sqrt(int s) const {
assert(at(0) == 1);
static const mint i2 = mint(2).inv();
V<mint> f{1},g{1},z{1};
for(int n=1;n<s;n*=2){
rep(i,n) z[i] *= z[i];
invfft(z);
V<mint> d(2*n);
rep(i,n) d[n+i] = z[i] - at(i) - at(n+i);
fft(d);
V<mint> g2(2*n);
rep(i,n) g2[i] = g[i];
fft(g2);
rep(i,n*2) d[i] *= g2[i];
invfft(d);
f.resize(n*2);
for(int i=n;i<n*2;i++) f[i] = -d[i] * i2;
if(n*2 >= s) break;
z = f;
fft(z);
V<mint> eps = g2;
rep(i,n*2) eps[i] *= z[i];
invfft(eps);
rep(i,n) eps[i] = 0;
fft(eps);
rep(i,n*2) eps[i] *= g2[i];
invfft(eps);
g.resize(n*2);
for(int i=n;i<n*2;i++) g[i] -= eps[i];
}
f.resize(s);
return f;
}
// Taylor Shift
// return f(x+c)
// O(N logN)
// verify: yosupo
Poly shift(mint c){
int n = size();
assert(si(fact) >= n); // please InitFact
V<mint> f(n); rep(i,n) f[i] = (*this)[i] * fact[i];
V<mint> g(n);
mint cpow = 1;
rep(i,n){g[i] = cpow * ifact[i]; cpow *= c;}
reverse(all(g));
V<mint> h = multiply(f,g);
Poly res(n); rep(i,n) res[i] = h[n-1+i] * ifact[i];
return res;
}
// 合成逆 mod x^s
// O(s^2 + s^1.5 log s)
// 方針: lagrange [x^i]g = (1/i [x^i-1](x/f)^i)
// (x/f)^i = (x/f)^jL (x/f)^k とすれば前計算はs^1.5回FFT
// 2つの積の一箇所求めるだけなのでO(s)
// z をかけまくったり z^L をかけまくったりするところはFFT消せるから高速化できる
// verify: https://www.luogu.com.cn/problem/P5809
Poly compositeInv(int s){
assert(at(0) == 0);
assert(at(1) != 0);
int L = 0;
while(L*L < s) L++;
Poly z0(s); rep(i,s) z0[i] = at(i+1);
Poly z = z0.inv(s); // = x/f
V<Poly> zi(L); // z^i
V<Poly> ziL(L); // z^iL
zi[0] = {1};
rep(i,L-1) zi[i+1] = (zi[i] * z).low(s);
auto zL = (zi[L-1] * z).low(s);
ziL[0] = {1};
rep(i,L-1) ziL[i+1] = (ziL[i] * zL).low(s);
Poly res(s);
rep1(k,s-1){
int i = k/L, j = k%L; // x^(iL+j)
rep(_,k) res[k] += ziL[i].at(_) * zi[j].at(k-1-_);
res[k] /= k;
}
return res;
}
};
// 合成 f○g mod x^s
// O(ns + sqrt(n)slogs)
// sを指定しないときはnm次全部返す O(n^2m)?
// \sum_k f_k g^k = \sum_k f_k g^iL+j = \sum_i g^iL * (\sum_j f_k g^j)
// verify: https://www.luogu.com.cn/problem/P5373
Poly<mint> composite(Poly<mint> f, Poly<mint> g, int s=-1){
int n = si(f)-1, m = si(g)-1;
if(s == -1) s = n*m+1;
int L = 0;
while(L*L <= n) L++;
V<Poly<mint>> gi(L); // g^i
V<Poly<mint>> giL(L); // g^iL
gi[0] = {1};
rep(i,L-1) gi[i+1] = (gi[i] * g).low(s);
auto gL = (gi[L-1] * g).low(s);
giL[0] = {1};
rep(i,L-1) giL[i+1] = (giL[i] * gL).low(s);
Poly<mint> res(s);
rep(i,L){
Poly<mint> z;
rep(j,L) if(i*L+j <= n) z += gi[j] * f[i*L+j];
res += (z * giL[i]).low(s);
}
return res;
}
ll norm_mod(ll a, ll m){
a %= m; if(a < 0) a += m;
return a;
}
//p: odd (not necessarily prime)
ll jacobi(ll a,ll p){
a = norm_mod(a,p);
auto sgn = [](ll x){ return x&1 ? -1 : 1; };
if(a == 0) return p == 1;
else if(a&1) return sgn(((p-1)&(a-1))>>1) * jacobi(p%a,a);
else return sgn(((p&15)*(p&15)-1)/8) * jacobi(a/2,p);
}
// p : prime
// 0 <= a < p
// return smaller solution
// if no solution, -1
ll sqrt_mod(ll a,ll p){
if(a == 0) return 0;
if(p == 2) return 1;
if(jacobi(a,p) == -1)return -1;
ll b,c;
for(b=0;;b++){
c = norm_mod(b*b-a,p);
if(jacobi(c,p) == -1) break;
}
auto mul = [&](pair<ll,ll> x, pair<ll,ll> y){
return pair<ll,ll>(norm_mod(x.fs*y.fs+x.sc*y.sc%p*c,p),norm_mod(x.fs*y.sc+x.sc*y.fs,p));
};
pair<ll,ll> x(b,1),res(1,0);
ll n = (p+1)/2;
while(n){
if(n&1) res = mul(res,x);
x = mul(x,x);
n >>= 1;
}
assert(res.sc == 0);
return min(res.fs, p-res.fs);
}
// 辞書順最小
// no solution -> {}
Poly<mint> sqrt(Poly<mint> f){
int n = f.size();
int ord = 0;
while(ord<n && !f[ord]) ord++;
if(ord == n) return {0};
if(ord&1) return {};
ll c0 = sqrt_mod(f[ord].v,mint::mod);
if(c0 == -1) return {};
int n_ = n-ord;
auto g = (Poly<mint>(f.begin()+ord,f.end())/f[ord]).sqrt(n_) * mint(c0);
Poly<mint> res(ord/2 + n_);
rep(i,n_) res[ord/2 + i] = g[i];
return res;
}
// Q log^2 Q ではある
// 高速なのはうまく subproduct tree を構築するらしい
// maroon https://judge.yosupo.jp/submission/3240 160ms
// verify: https://judge.yosupo.jp/submission/45006 950ms
template<class mint>
V<mint> MultipointEval(const Poly<mint>& f, V<mint> a){
int Q = a.size();
int s = 1; while(s < Q) s *= 2;
V<Poly<mint>> g(s+s,{1});
rep(i,Q) g[s+i] = {-a[i],1};
for(int i=s-1;i>0;i--) g[i] = g[i*2] * g[i*2+1];
g[1] = f % g[1];
for(int i=2;i<s+Q;i++) g[i] = g[i>>1] % g[i];
V<mint> res(Q);
rep(i,Q) res[i] = g[s+i][0];
return res;
}
// N log^2 N ではある
// 高速なのはうまく subうんぬん
template<class mint>
Poly<mint> interpolate(const V<mint>& x, const V<mint>& y){
int n = si(x);
int s = 1; while(s<n) s*=2;
V<Poly<mint>> g(s+s,{1}), h(s+s);
rep(i,n) g[s+i] = {-x[i],1};
for(int i=s-1;i>0;i--) g[i] = g[i*2] * g[i*2+1];
h[1] = g[1].diff();
for(int i=2;i<s+n;i++) h[i] = h[i>>1] % g[i];
rep(i,n) h[s+i] = {y[i] / h[s+i][0]};
for(int i=s-1;i>0;i--) h[i] = h[i*2]*g[i*2+1] + h[i*2+1]*g[i*2];
return h[1];
}
// [x^p] f/g
// O(n logn logp)
// O(f logf + g logg logn) (f が大きくてもややOK)
// verified: https://ac.nowcoder.com/acm/contest/11259/H
// hos,divAt : https://ac.nowcoder.com/acm/contest/view-submission?submissionId=48462458
template<class T>
T divAt(Poly<T> f, Poly<T> g, ll p){
assert(g.at(0));
while(p){
auto gm = g;
for(int i=1;i<si(g);i+=2) gm[i] = -gm[i];
auto f2 = f*gm;
auto g2 = g*gm;
f.clear();g.clear();
for(int i=p&1;i<si(f2);i+=2) f.set(i/2,f2[i]);
for(int i=0;i<si(g2);i+=2) g.set(i/2,g2[i]);
p /= 2;
}
return f.at(0)/g.at(0);
}
/*
input:
はじめ d 項: a_0, a_1, .., a_{d-1}
d+1 項 reccurence: c_0 * a_{i+d} + .. + c_d * a_i = 0
aを無駄に与えても良い(足りないと、カス)
ll k
output:
a_k
O(d logd logk)
verified: https://judge.yosupo.jp/problem/find_linear_recurrence
*/
template<class T>
T linearRecurrenceAt(V<T> a, V<T> c, ll k){
assert(!c.empty() && c[0]);
int d = si(c) - 1;
assert(si(a) >= d);
return divAt((Poly<T>(a.begin(),a.begin()+d) * Poly<T>(c)).low(d), Poly<T>(c), k);
}
// return f(K+1)
// f[k] = 0^k + .. + n^k
// \sum_{k>=0} f[k] x^k/k! = e^0x + .. + e^nx = 1-e^(n+1)x / 1-e^x
// O(KlogK)
// 0^0 = 1
// keyword: faulhaber ファウルハーバー
vector<mint> SumOfPower(mint n, int K){
assert(si(fact) > K);
Poly<mint> a(K+1),b(K+1);
mint pw = 1;
rep1(i,K+1){
pw *= n+1;
a[i-1] = ifact[i];
b[i-1] = ifact[i] * pw;
}
auto f = b*a.inv(K+1);
V<mint> res(K+1);
rep(k,K+1) res[k] = f[k] * fact[k];
return res;
}
#line 7 "2794.cpp"
void TEST(){
int N; cin >> N;
V<int> p(N); iota(all(p),0);
V<int> f(1<<(N-1));
do{
bool valid = true;
rep(k,N) rep(j,k) rep(i,j) if(p[i]<p[j] && p[j]<p[k]) valid = false;
if(!valid) continue;
int s = 0; rep(i,N-1) if(p[i] < p[i+1]) s |= 1<<i;
f[s]++;
}while(next_permutation(all(p)));
rep(s,si(f)){
rep(i,N-1){
if(s&1<<i) cout << '<';
else cout << '>';
}
if(f[s]) cout << " : " << f[s];
cout << endl;
}
cout << endl;
rep(s,si(f)){
rep(i,N-1){
if(s&1<<i) cout << '<';
else cout << '?';
}
mint acc = 0;
rep(t,si(f)) if((t&s) == s) acc += f[t];
if(acc) cout << " : " << acc;
cout << endl;
}
exit(0);
}
mint Cat(int n){
return Choose(n+n,n) * invs[n+1];
}
mint solve(string s){
int N = si(s) + 1;
if(count(all(s),'<') == 0){
return 0;
}
rep(i,N-2) if(s[i] == '<' && s[i+1] == '<'){
return 0;
}
V<int> as = {-2};
rep(i,N-1) if(s[i] == '<') as.eb(i);
as.eb(N);
using poly = Poly<mint>;
V<poly> ps;
rep(i,si(as)-1){
int n = as[i+1] - as[i] - 2;
poly p;
rep(k,n/2+1) p.set(k,Choose(n-k, k));
ps.eb(p);
}
auto mul = [&](auto&& self, int l, int r) -> poly {
if(r-l == 1) return ps[l];
int m = (l+r)/2;
return self(self,l,m) * self(self,m,r);
};
auto f = mul(mul,0,si(ps));
int A = si(as) - 2;
mint res = 0;
rep(k,si(f)) res += f[k] * Cat(N-A-k) * (k&1 ? -1 : 1);
return res;
}
int main(){
cin.tie(0);
ios::sync_with_stdio(false); //DON'T USE scanf/printf/puts !!
cout << fixed << setprecision(20);
InitFact(500000);
// TEST();
int N; string s; cin >> N >> s;
cout << solve(s) << endl;
}