結果
問題 | No.1302 Random Tree Score |
ユーザー |
👑 ![]() |
提出日時 | 2022-01-02 04:58:33 |
言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
結果 |
AC
|
実行時間 | 206 ms / 3,000 ms |
コード長 | 22,465 bytes |
コンパイル時間 | 3,746 ms |
コンパイル使用メモリ | 234,976 KB |
最終ジャッジ日時 | 2025-01-27 08:27:12 |
ジャッジサーバーID (参考情報) |
judge1 / judge2 |
(要ログイン)
ファイルパターン | 結果 |
---|---|
sample | AC * 3 |
other | AC * 14 |
ソースコード
//#define _GLIBCXX_DEBUG#include<bits/stdc++.h>using namespace std;#define endl '\n'#define lfs cout<<fixed<<setprecision(10)#define ALL(a) (a).begin(),(a).end()#define ALLR(a) (a).rbegin(),(a).rend()#define UNIQUE(a) (a).erase(unique((a).begin(),(a).end()),(a).end())#define spa << " " <<#define fi first#define se second#define MP make_pair#define MT make_tuple#define PB push_back#define EB emplace_back#define rep(i,n,m) for(ll i = (n); i < (ll)(m); i++)#define rrep(i,n,m) for(ll i = (ll)(m) - 1; i >= (ll)(n); i--)using ll = long long;using ld = long double;const ll MOD1 = 1e9+7;const ll MOD9 = 998244353;const ll INF = 1e18;using P = pair<ll, ll>;template<typename T> using PQ = priority_queue<T>;template<typename T> using QP = priority_queue<T,vector<T>,greater<T>>;template<typename T1, typename T2>bool chmin(T1 &a,T2 b){if(a>b){a=b;return true;}else return false;}template<typename T1, typename T2>bool chmax(T1 &a,T2 b){if(a<b){a=b;return true;}else return false;}ll median(ll a,ll b, ll c){return a+b+c-max({a,b,c})-min({a,b,c});}void ans1(bool x){if(x) cout<<"Yes"<<endl;else cout<<"No"<<endl;}void ans2(bool x){if(x) cout<<"YES"<<endl;else cout<<"NO"<<endl;}void ans3(bool x){if(x) cout<<"Yay!"<<endl;else cout<<":("<<endl;}template<typename T1,typename T2>void ans(bool x,T1 y,T2 z){if(x)cout<<y<<endl;else cout<<z<<endl;}template<typename T1,typename T2,typename T3>void anss(T1 x,T2 y,T3 z){ans(x!=y,x,z);};template<typename T>void debug(const T &v,ll h,ll w,string sv=" "){for(ll i=0;i<h;i++){cout<<v[i][0];for(ll j=1;j<w;j++)cout<<sv<<v[i][j];cout<<endl;}};template<typename T>void debug(const T &v,ll n,string sv=" "){if(n!=0)cout<<v[0];for(ll i=1;i<n;i++)cout<<sv<<v[i];cout<<endl;};template<typename T>void debug(const vector<T>&v){debug(v,v.size());}template<typename T>void debug(const vector<vector<T>>&v){for(auto &vv:v)debug(vv,vv.size());}template<typename T>void debug(stack<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(queue<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(deque<T> st){while(!st.empty()){cout<<st.front()<<" ";st.pop_front();}cout<<endl;}template<typename T>void debug(PQ<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(QP<T> st){while(!st.empty()){cout<<st.top()<<" ";st.pop();}cout<<endl;}template<typename T>void debug(const set<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}template<typename T>void debug(const multiset<T>&v){for(auto z:v)cout<<z<<" ";cout<<endl;}template<typename T,size_t size>void debug(const array<T, size> &a){for(auto z:a)cout<<z<<" ";cout<<endl;}template<typename T,typename V>void debug(const map<T,V>&v){for(auto z:v)cout<<"["<<z.first<<"]="<<z.second<<",";cout<<endl;}template<typename T>vector<vector<T>>vec(ll x, ll y, T w){vector<vector<T>>v(x,vector<T>(y,w));return v;}ll gcd(ll x,ll y){ll r;while(y!=0&&(r=x%y)!=0){x=y;y=r;}return y==0?x:y;}vector<ll>dx={1,-1,0,0,1,1,-1,-1};vector<ll>dy={0,0,1,-1,1,-1,1,-1};template<typename T>vector<T> make_v(size_t a,T b){return vector<T>(a,b);}template<typename... Ts>auto make_v(size_t a,Ts... ts){return vector<decltype(make_v(ts...))>(a,make_v(ts...));}template<typename T1, typename T2>ostream &operator<<(ostream &os, const pair<T1, T2>&p){return os << p.first << " " << p.second;}template<typename T>ostream &operator<<(ostream &os, const vector<T> &v){for(auto &z:v)os << z << " ";cout<<"|"; return os;}template<typename T>void rearrange(vector<int>&ord, vector<T>&v){auto tmp = v;for(int i=0;i<tmp.size();i++)v[i] = tmp[ord[i]];}template<typename Head, typename... Tail>void rearrange(vector<int>&ord,Head&& head, Tail&&... tail){rearrange(ord, head);rearrange(ord, tail...);}template<typename T> vector<int> ascend(const vector<T>&v){vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]<v[j];});return ord;}template<typename T> vector<int> descend(const vector<T>&v){vector<int>ord(v.size());iota(ord.begin(),ord.end(),0);sort(ord.begin(),ord.end(),[&](int i,int j){return v[i]>v[j];});return ord;}ll FLOOR(ll n,ll div){assert(div>0);return n>=0?n/div:(n-div+1)/div;}ll CEIL(ll n,ll div){assert(div>0);return n>=0?(n+div-1)/div:n/div;}ll digitsum(ll n){ll ret=0;while(n){ret+=n%10;n/=10;}return ret;}ll modulo(ll n,ll d){return (n%d+d)%d;};template<typename T>T min(const vector<T>&v){return *min_element(v.begin(),v.end());}template<typename T>T max(const vector<T>&v){return *max_element(v.begin(),v.end());}template<typename T>T acc(const vector<T>&v){return accumulate(v.begin(),v.end(),T(0));};template<typename T>T reverse(const T &v){return T(v.rbegin(),v.rend());};//mt19937 mt(chrono::steady_clock::now().time_since_epoch().count());int popcount(ll x){return __builtin_popcountll(x);};int poplow(ll x){return __builtin_ctzll(x);};int pophigh(ll x){return 63 - __builtin_clzll(x);};template<typename T>T poll(queue<T> &q){auto ret=q.front();q.pop();return ret;};template<typename T>T poll(priority_queue<T> &q){auto ret=q.top();q.pop();return ret;};template<typename T>T poll(QP<T> &q){auto ret=q.top();q.pop();return ret;};template<typename T>T poll(stack<T> &s){auto ret=s.top();s.pop();return ret;};ll MULT(ll x,ll y){if(LLONG_MAX/x<=y)return LLONG_MAX;return x*y;}ll POW2(ll x, ll k){ll ret=1,mul=x;while(k){if(mul==LLONG_MAX)return LLONG_MAX;if(k&1)ret=MULT(ret,mul);mul=MULT(mul,mul);k>>=1;}return ret;}ll POW(ll x, ll k){ll ret=1;for(int i=0;i<k;i++){if(LLONG_MAX/x<=ret)return LLONG_MAX;ret*=x;}return ret;}template< typename T = int >struct edge {int to;T cost;int id;edge():id(-1){};edge(int to, T cost = 1, int id = -1):to(to), cost(cost), id(id){}operator int() const { return to; }};template<typename T>using Graph = vector<vector<edge<T>>>;template<typename T>Graph<T>revgraph(const Graph<T> &g){Graph<T>ret(g.size());for(int i=0;i<g.size();i++){for(auto e:g[i]){int to = e.to;e.to = i;ret[to].push_back(e);}}return ret;}template<typename T>Graph<T> readGraph(int n,int m,int indexed=1,bool directed=false,bool weighted=false){Graph<T> ret(n);for(int es = 0; es < m; es++){int u,v;T w=1;cin>>u>>v;u-=indexed,v-=indexed;if(weighted)cin>>w;ret[u].emplace_back(v,w,es);if(!directed)ret[v].emplace_back(u,w,es);}return ret;}template<typename T>Graph<T> readParent(int n,int indexed=1,bool directed=true){Graph<T>ret(n);for(int i=1;i<n;i++){int p;cin>>p;p-=indexed;ret[p].emplace_back(i);if(!directed)ret[i].emplace_back(p);}return ret;}template< int mod >struct ModInt {int x;ModInt() : x(0) {}ModInt(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}ModInt &operator+=(const ModInt &p) {if((x += p.x) >= mod) x -= mod;return *this;}ModInt &operator-=(const ModInt &p) {if((x += mod - p.x) >= mod) x -= mod;return *this;}ModInt &operator*=(const ModInt &p) {x = (int) (1LL * x * p.x % mod);return *this;}ModInt &operator/=(const ModInt &p) {*this *= p.inverse();return *this;}ModInt operator-() const { return ModInt(-x); }friend ModInt operator+(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) += rhs;}friend ModInt operator-(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) -= rhs;}friend ModInt operator*(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) *= rhs;}friend ModInt operator/(const ModInt& lhs, const ModInt& rhs) {return ModInt(lhs) /= rhs;}bool operator==(const ModInt &p) const { return x == p.x; }bool operator!=(const ModInt &p) const { return x != p.x; }ModInt inverse() const {int a = x, b = mod, u = 1, v = 0, t;while(b > 0) {t = a / b;swap(a -= t * b, b);swap(u -= t * v, v);}return ModInt(u);}ModInt pow(int64_t n) const {ModInt ret(1), mul(x);while(n > 0) {if(n & 1) ret *= mul;mul *= mul;n >>= 1;}return ret;}friend ostream &operator<<(ostream &os, const ModInt &p) {return os << p.x;}friend istream &operator>>(istream &is, ModInt &a) {int64_t t;is >> t;a = ModInt< mod >(t);return (is);}static int get_mod() { return mod; }};template< typename T >struct Combination {vector< T > _fact, _rfact, _inv;Combination(ll sz) : _fact(sz + 1), _rfact(sz + 1), _inv(sz + 1) {_fact[0] = _rfact[sz] = _inv[0] = 1;for(ll i = 1; i <= sz; i++) _fact[i] = _fact[i - 1] * i;_rfact[sz] /= _fact[sz];for(ll i = sz - 1; i >= 0; i--) _rfact[i] = _rfact[i + 1] * (i + 1);for(ll i = 1; i <= sz; i++) _inv[i] = _rfact[i] * _fact[i - 1];}inline T fact(ll k) const { return _fact[k]; }inline T rfact(ll k) const { return _rfact[k]; }inline T inv(ll k) const { return _inv[k]; }T P(ll n, ll r) const {if(r < 0 || n < r) return 0;return fact(n) * rfact(n - r);}T C(ll p, ll q) const {if(q < 0 || p < q) return 0;return fact(p) * rfact(q) * rfact(p - q);}T RC(ll p, ll q) const {if(q < 0 || p < q) return 0;return rfact(p) * fact(q) * fact(p - q);}T H(ll n, ll r) const {if(n < 0 || r < 0) return (0);return r == 0 ? 1 : C(n + r - 1, r);}};using modint = ModInt< MOD9 >;modint pow(ll n, ll x){return modint(n).pow(x);}modint pow(modint n, ll x){return n.pow(x);}//using modint=ld;using Comb=Combination<modint>;template< typename Mint >struct NumberTheoreticTransformFriendlyModInt {vector< Mint > dw, idw;int max_base;Mint root;NumberTheoreticTransformFriendlyModInt() {const unsigned mod = Mint::get_mod();assert(mod >= 3 && mod % 2 == 1);auto tmp = mod - 1;max_base = 0;while(tmp % 2 == 0) tmp >>= 1, max_base++;root = 2;while(root.pow((mod - 1) >> 1) == 1) root += 1;assert(root.pow(mod - 1) == 1);dw.resize(max_base);idw.resize(max_base);for(int i = 0; i < max_base; i++) {dw[i] = -root.pow((mod - 1) >> (i + 2));idw[i] = Mint(1) / dw[i];}}void ntt(vector< Mint > &a) {const int n = (int) a.size();assert((n & (n - 1)) == 0);assert(__builtin_ctz(n) <= max_base);for(int m = n; m >>= 1;) {Mint w = 1;for(int s = 0, k = 0; s < n; s += 2 * m) {for(int i = s, j = s + m; i < s + m; ++i, ++j) {auto x = a[i], y = a[j] * w;a[i] = x + y, a[j] = x - y;}w *= dw[__builtin_ctz(++k)];}}}void intt(vector< Mint > &a, bool f = true) {const int n = (int) a.size();assert((n & (n - 1)) == 0);assert(__builtin_ctz(n) <= max_base);for(int m = 1; m < n; m *= 2) {Mint w = 1;for(int s = 0, k = 0; s < n; s += 2 * m) {for(int i = s, j = s + m; i < s + m; ++i, ++j) {auto x = a[i], y = a[j];a[i] = x + y, a[j] = (x - y) * w;}w *= idw[__builtin_ctz(++k)];}}if(f) {Mint inv_sz = Mint(1) / n;for(int i = 0; i < n; i++) a[i] *= inv_sz;}}vector< Mint > multiply(vector< Mint > a, vector< Mint > b) {int need = a.size() + b.size() - 1;int nbase = 1;while((1 << nbase) < need) nbase++;int sz = 1 << nbase;a.resize(sz, 0);b.resize(sz, 0);ntt(a);ntt(b);Mint inv_sz = Mint(1) / sz;for(int i = 0; i < sz; i++) a[i] *= b[i] * inv_sz;intt(a, false);a.resize(need);return a;}};template< typename T >struct FormalPowerSeries : vector< T > {using vector< T >::vector;using P = FormalPowerSeries;using MULT = function< P(P, P) >;using FFT = function< void(P &) >;using SQRT = function< T(T) >;static MULT &get_mult() {static MULT mult = nullptr;return mult;}static void set_mult(MULT f) {get_mult() = f;}static FFT &get_fft() {static FFT fft = nullptr;return fft;}static FFT &get_ifft() {static FFT ifft = nullptr;return ifft;}static void set_fft(FFT f, FFT g) {get_fft() = f;get_ifft() = g;}static SQRT &get_sqrt() {static SQRT sqr = nullptr;return sqr;}static void set_sqrt(SQRT sqr) {get_sqrt() = sqr;}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 T &r) {if(this->empty()) this->resize(1);(*this)[0] += r;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];//shrink();return *this;}P &operator-=(const T &r) {if(this->empty()) this->resize(1);(*this)[0] -= r;//shrink();return *this;}P &operator*=(const T &v) {const int n = (int) this->size();for(int k = 0; k < n; k++) (*this)[k] *= v;return *this;}P &operator*=(const P &r) {if(this->empty() || r.empty()) {this->clear();return *this;}if(min(this->size(), r.size()) < 5 || get_mult() == nullptr){P ret(this->size() + r.size() - 1);for(int i = 0; i < this->size(); i++){for(int j = 0; j < r.size(); j++){ret[i + j] += (*this)[i] * r[j];}}return *this = ret;}return *this = get_mult()(*this, r);}P &operator%=(const P &r) { return *this -= *this / r * 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 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 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 pre(int sz) const { return P(begin(*this), begin(*this) + min((int) this->size(), sz)); }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;}P rev(int deg = -1) const {P ret(*this);if(deg != -1) ret.resize(deg, T(0));reverse(begin(ret), end(ret));return ret;}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;}// F(0) must not be 0P inv(int deg = -1) const {assert(((*this)[0]) != T(0));const int n = (int) this->size();if(deg == -1) deg = n;if(get_fft() != nullptr) {P ret(*this);ret.resize(deg, T(0));return ret.inv_fast();}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);}// F(0) must be 1P log(int deg = -1) const {assert((*this)[0] == 1);const int n = (int) this->size();if(deg == -1) deg = n;return (this->diff() * this->inv(deg)).pre(deg - 1).integral();}P sqrt(int deg = -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);if(ret.empty()) return {};ret = ret << (i / 2);if(ret.size() < deg) ret.resize(deg, T(0));return ret;}}return P(deg, 0);}P ret;if(get_sqrt() == nullptr) {assert((*this)[0] == T(1));ret = {T(1)};} else {auto sqr = get_sqrt()((*this)[0]);if(sqr * sqr != (*this)[0]) return {};ret = {T(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);}// F(0) must be 0P exp(int deg = -1) const {assert((*this)[0] == T(0));const int n = (int) this->size();if(deg == -1) deg = n;if(get_fft() != nullptr) {P ret(*this);ret.resize(deg, T(0));return ret.exp_rec();}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);}P online_convolution_exp(const P &conv_coeff) const {const int n = (int) conv_coeff.size();assert((n & (n - 1)) == 0);vector< P > conv_ntt_coeff;auto& fft = get_fft();auto& ifft = get_ifft();for(int i = n; i >= 1; i >>= 1) {P g(conv_coeff.pre(i));fft(g);conv_ntt_coeff.emplace_back(g);}P conv_arg(n), conv_ret(n);auto rec = [&](auto rec, int l, int r, int d) -> void {if(r - l <= 16) {for(int i = l; i < r; i++) {T sum = 0;for(int j = l; j < i; j++) sum += conv_arg[j] * conv_coeff[i - j];conv_ret[i] += sum;conv_arg[i] = i == 0 ? T(1) : conv_ret[i] / i;}} else {int m = (l + r) / 2;rec(rec, l, m, d + 1);P pre(r - l);for(int i = 0; i < m - l; i++) pre[i] = conv_arg[l + i];fft(pre);for(int i = 0; i < r - l; i++) pre[i] *= conv_ntt_coeff[d][i];ifft(pre);for(int i = 0; i < r - m; i++) conv_ret[m + i] += pre[m + i - l];rec(rec, m, r, d + 1);}};rec(rec, 0, n, 0);return conv_arg;}P exp_rec() const {assert((*this)[0] == T(0));const int n = (int) this->size();int m = 1;while(m < n) m *= 2;P conv_coeff(m);for(int i = 1; i < n; i++) conv_coeff[i] = (*this)[i] * i;return online_convolution_exp(conv_coeff).pre(n);}P inv_fast() const {assert(((*this)[0]) != T(0));const int n = (int) this->size();P res{T(1) / (*this)[0]};for(int d = 1; d < n; d <<= 1) {P f(2 * d), g(2 * d);for(int j = 0; j < min(n, 2 * d); j++) f[j] = (*this)[j];for(int j = 0; j < d; j++) g[j] = res[j];get_fft()(f);get_fft()(g);for(int j = 0; j < 2 * d; j++) f[j] *= g[j];get_ifft()(f);for(int j = 0; j < d; j++) {f[j] = 0;f[j + d] = -f[j + d];}get_fft()(f);for(int j = 0; j < 2 * d; j++) f[j] *= g[j];get_ifft()(f);for(int j = 0; j < d; j++) f[j] = res[j];res = f;}return res.pre(n);}P pow(int64_t k, int deg = -1) const {const int n = (int) this->size();if(deg == -1) deg = n;for(int i = 0; i < n; i++) {if((*this)[i] != T(0)) {T rev = T(1) / (*this)[i];P ret = (((*this * rev) >> i).log(deg) * k).exp(deg) * ((*this)[i].pow(k));if(i * k > deg) return P(deg, T(0));ret = (ret << (i * k)).pre(deg);if(ret.size() < deg) ret.resize(deg, T(0));return ret;}}return *this;}T eval(T x) const {T r = 0, w = 1;for(auto &v : *this) {r += w * v;w *= x;}return r;}P pow_mod(int64_t n, P mod) const {P modinv = mod.rev().inv();auto get_div = [&](P base) {if(base.size() < mod.size()) {base.clear();return base;}int n = base.size() - mod.size() + 1;return (base.rev().pre(n) * modinv.pre(n)).pre(n).rev(n);};P x(*this), ret{1};while(n > 0) {if(n & 1) {ret *= x;ret -= get_div(ret) * mod;}x *= x;x -= get_div(x) * mod;n >>= 1;}return ret;}void mul(vector<pair<int, T>> g, bool extend = false){if(extend)this->resize(this->size() + g.back().first);int n = this->size();int d = g[0].first;T c = g[0].second;if(d == 0)g.erase(g.begin());else c = 0;for(int i = n - 1; i >= 0; i--){(*this)[i] *= c;for(auto z : g){if(z.first > i)continue;(*this)[i] += (*this)[i-z.first] * z.second;}}}void div(vector<pair<int, T>>g){//定数項は非ゼロint n = this->size();int d = g[0].first;T c = g[0].second;c = T(1) / c;g.erase(g.begin());for(int i = 0; i < n; i++){for(auto z : g){if(z.first > i)continue;(*this)[i] -= (*this)[i-z.first] * z.second;}(*this)[i] *= c;}}};/*using FPS=FormalPowerSeries<modint>;ArbitraryModConvolution<modint> ntt;auto mult=[&](const FPS &x,const FPS &y){auto ret = ntt.multiply(x,y);return FPS(ret.begin(),ret.end());};FPS::set_mult(mult);*/int main(){cin.tie(nullptr);ios_base::sync_with_stdio(false);ll res=0,buf=0;bool judge = true;using FPS=FormalPowerSeries<modint>;NumberTheoreticTransformFriendlyModInt<modint> ntt;auto mult=[&](const FPS &x,const FPS &y){auto ret = ntt.multiply(x,y);return FPS(ret.begin(),ret.end());};FPS::set_mult(mult);FPS::set_fft([&](FPS &a){return ntt.ntt(a);},[&](FPS &b){return ntt.intt(b);});ll n;cin>>n;FPS f(n);Comb comb(n+2);rep(i,0,n)f[i]=(i+1)*comb.rfact(i);f=f.pow(n,-1);modint ret=f[n-2]*comb.fact(n-2)/pow(n,n-2);cout<<ret<<endl;return 0;}