結果
| 問題 | No.2595 Parsing Challenge |
| ユーザー |
👑  tute7627
|
| 提出日時 | 2023-12-23 00:49:18 |
| 言語 | C++17 (gcc 12.3.0 + boost 1.83.0) |
| 結果 |
WA
|
| 実行時間 | - |
| コード長 | 32,288 bytes |
| コンパイル時間 | 3,052 ms |
| コンパイル使用メモリ | 240,876 KB |
| 実行使用メモリ | 191,968 KB |
| 最終ジャッジ日時 | 2024-09-27 11:46:19 |
| 合計ジャッジ時間 | 6,524 ms |
|
ジャッジサーバーID （参考情報） |
judge3 / judge1 |
（要ログイン）
テストケース
テストケース表示| 入力 | 結果 | 実行時間 実行使用メモリ |
|---|---|---|
| testcase_00 | WA | - |
| testcase_01 | WA | - |
| testcase_02 | WA | - |
| testcase_03 | WA | - |
| testcase_04 | WA | - |
| testcase_05 | WA | - |
| testcase_06 | WA | - |
| testcase_07 | WA | - |
| testcase_08 | WA | - |
| testcase_09 | WA | - |
| testcase_10 | WA | - |
| testcase_11 | WA | - |
| testcase_12 | WA | - |
| testcase_13 | WA | - |
| testcase_14 | WA | - |
| testcase_15 | WA | - |
| testcase_16 | WA | - |
| testcase_17 | WA | - |
| testcase_18 | WA | - |
| testcase_19 | WA | - |
| testcase_20 | WA | - |
| testcase_21 | WA | - |
| testcase_22 | WA | - |
| testcase_23 | WA | - |
| testcase_24 | WA | - |
| testcase_25 | WA | - |
| testcase_26 | WA | - |
| testcase_27 | WA | - |
| testcase_28 | WA | - |
| testcase_29 | WA | - |
| testcase_30 | WA | - |
| testcase_31 | WA | - |
| testcase_32 | WA | - |
| testcase_33 | WA | - |
| testcase_34 | WA | - |
| testcase_35 | WA | - |
| testcase_36 | WA | - |
| testcase_37 | WA | - |
| testcase_38 | WA | - |
| testcase_39 | WA | - |
| testcase_40 | WA | - |
| testcase_41 | WA | - |
| testcase_42 | WA | - |
| testcase_43 | WA | - |
| testcase_44 | WA | - |
| testcase_45 | WA | - |
| testcase_46 | WA | - |
| testcase_47 | WA | - |
| testcase_48 | WA | - |
| testcase_49 | WA | - |
| testcase_50 | WA | - |
| testcase_51 | WA | - |
| testcase_52 | WA | - |
| testcase_53 | WA | - |
| testcase_54 | WA | - |
| testcase_55 | WA | - |
| testcase_56 | WA | - |
| testcase_57 | WA | - |
| testcase_58 | WA | - |
| testcase_59 | WA | - |
ソースコード
//#define _GLIBCXX_DEBUG
//#pragma GCC target("avx2")
//#pragma GCC optimize("O3")
//#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>
using namespace std;
#ifdef LOCAL
#include <debug_print.hpp>
#define OUT(...) debug_print::multi_print(#__VA_ARGS__, __VA_ARGS__)
#else
#define OUT(...) (static_cast<void>(0))
#endif
#define endl '\n'
#define lfs cout<<fixed<<setprecision(15)
#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;}
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){os<<"[";for(auto &z:v)os << z << ",";os<<"]"; 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 make_pair(v[i],i)<make_pair(v[j],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 make_pair(v[i],-i)>make_pair(v[j],-j);});
return ord;
}
template<typename T> vector<T> inv_perm(const vector<T>&ord){
vector<T>inv(ord.size());
for(int i=0;i<ord.size();i++)inv[ord[i]] = i;
return inv;
}
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;}
std::ostream &operator<<(std::ostream &dest, __int128_t value) {
std::ostream::sentry s(dest);
if (s) {
__uint128_t tmp = value < 0 ? -value : value;
char buffer[128];
char *d = std::end(buffer);
do {
--d;
*d = "0123456789"[tmp % 10];
tmp /= 10;
} while (tmp != 0);
if (value < 0) {
--d;
*d = '-';
}
int len = std::end(buffer) - d;
if (dest.rdbuf()->sputn(d, len) != len) {
dest.setstate(std::ios_base::badbit);
}
}
return dest;
}
namespace converter{
int dict[500];
const string lower="abcdefghijklmnopqrstuvwxyz";
const string upper="ABCDEFGHIJKLMNOPQRSTUVWXYZ";
const string digit="0123456789";
const string digit1="123456789";
void regi_str(const string &t){
for(int i=0;i<t.size();i++){
dict[t[i]]=i;
}
}
void regi_int(const string &t){
for(int i=0;i<t.size();i++){
dict[i]=t[i];
}
}
vector<int>to_int(const string &s,const string &t){
regi_str(t);
vector<int>ret(s.size());
for(int i=0;i<s.size();i++){
ret[i]=dict[s[i]];
}
return ret;
}
vector<int>to_int(const string &s){
auto t=s;
sort(t.begin(),t.end());
t.erase(unique(t.begin(),t.end()),t.end());
return to_int(s,t);
}
vector<vector<int>>to_int(const vector<string>&s,const string &t){
regi_str(t);
vector<vector<int>>ret(s.size(),vector<int>(s[0].size()));
for(int i=0;i<s.size();i++){
for(int j=0;j<s[0].size();j++){
ret[i][j]=dict[s[i][j]];
}
}
return ret;
}
vector<vector<int>>to_int(const vector<string>&s){
string t;
for(int i=0;i<s.size();i++){
t+=s[i];
}
sort(t.begin(),t.end());t.erase(unique(t.begin(),t.end()),t.end());
return to_int(s,t);
}
string to_str(const vector<int>&s,const string &t){
regi_int(t);
string ret;
for(auto z:s)ret+=dict[z];
return ret;
}
vector<string> to_str(const vector<vector<int>>&s,const string &t){
regi_int(t);
vector<string>ret(s.size());
for(int i=0;i<s.size();i++){
for(auto z:s[i])ret[i]+=dict[z];
}
return ret;
}
}
template< typename T = int >
struct edge {
int to;
T cost;
int id;
edge():to(-1),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<typename T>
struct HLD{
using D=long long;
int n;
vector<int>sz;//部分木サイズ
vector<D>dep;
vector<int>par;
vector<int>head;
Graph<T> &g;//隣接リスト
vector<edge<T>>edges;//データ構造に乗せるedge列
vector<int>in,out;//[in,out)で部分木、[ina,inb]でa~bのパス(aが上)
vector<int>comp;//連結成分の根
//inは頂点のindexを表す。また、edge列の下側の頂点である
HLD(Graph<T> &g,int r=-1):g(g),n(g.size()){
hld_build(r);
}
void hld_build(int root = -1){
in.assign(n,-1);out.assign(n,-1);dep.assign(n,0);
par.assign(n,-1);head.assign(n,-1);sz.assign(n,-1);comp.assign(n,-1);
edges.assign(n,edge<T>());
if(root == -1){//根がどこでも良い場合(森でも可)
for(int i=0;i<n;i++){
if(sz[i] == -1){
head[i] = i;
dfs_sz(i, 0, i);
dfs_hld(i);
}
}
}
else{
head[root] = root;
dfs_sz(root, 0, root);
dfs_hld(root);
}
}
void dfs_sz(int k, D d,int r){
sz[k] = 1;
comp[k] = r;
dep[k] = d;
for(auto &e: g[k]){
if(e.to == par[k])continue;
par[e.to] = k;
dfs_sz(e.to, d+e.cost, r);
sz[k] += sz[e.to];
if(g[k][0].to==par[k]||sz[e.to] > sz[g[k][0].to])swap(e, g[k][0]);
}
}
int time = 0;
void dfs_hld(int k){
in[k] = time++;
for(auto e:g[k]){
if(e.to == par[k])continue;
head[e.to] = (e.to == g[k][0].to ? head[k]: e.to);
edges[time] = e;
dfs_hld(e.to);
}
out[k] = time;
}
int lca(int p,int q){
while(1){
if(in[p] < in[q])swap(p,q);
if(head[p] == head[q])return q;
p = par[head[p]];
}
}
vector<pair<int,int>>query_path(int p,int q,bool isEdge){
int r=lca(p,q);
vector<pair<int,int>>ret;
for(int i=0;i<2;i++){
if(i == 1)swap(p,q);
while(1){
if(isEdge&&p==r)break;
if(head[p]==head[r]){
ret.emplace_back(in[r]+(isEdge?1:i),in[p]+1);
break;
}
ret.emplace_back(in[head[p]],in[p]+1);
p = par[head[p]];
}
}
return ret;
}
vector<vector<pair<int,int>>>query_order_path(int p,int q,bool isEdge){
//非可換クエリ用、配列0を順番を反転したデータ構造に、配列1を通常のデータ構造に
vector<vector<pair<int,int>>>ret(2);
int r=lca(p,q);
for(int i=0;i<2;i++){
if(i == 1)swap(p,q);
while(1){
if(isEdge&&p==r)break;
if(head[p]==head[r]){
if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[r]+(isEdge?1:i)));
else ret[i].emplace_back(in[r]+(isEdge?1:i),in[p]+1);
break;
}
if(i==0) ret[i].emplace_back(n-(in[p]+1),n-(in[head[p]]));
else ret[i].emplace_back(in[head[p]],in[p]+1);
p = par[head[p]];
}
}
reverse(ret[1].begin(), ret[1].end());
return ret;
}
pair<int,int>query_subtree(int p,bool isEdge){
return make_pair(in[p]+isEdge,out[p]);
}
//uのv方向の子 子孫関係は前もって確認すること(in,outを見る)
int child(int u,int v)const{
while(1){
if(head[u]==head[v]){
v=g[u][0].to;
break;
}
v=head[v];
if(par[v]==u)break;
v=par[v];
}
return v;
}
//uをv方向に一つ進めた頂点
int move(int u,int v)const{
assert(u!=v);
if(in[u]<in[v]&&in[v]<out[u])return child(u,v);
else return par[u];
}
D dist(int u,int v){
return dep[u]+dep[v]-2*dep[lca(u,v)];
}
vector<int>rev_in;
int climb(int u,int k){
if(rev_in.empty()){
rev_in.resize(n);
for(int i=0;i<n;i++)rev_in[in[i]]=i;
}
int nd=max<int>(dep[u]-k, 0);
while(dep[u]>nd){
if(dep[head[u]]>nd){
u=par[head[u]];
}
else{
u=rev_in[in[head[u]]+nd-dep[head[u]]];
}
}
return u;
}
int jump(int from,int to, int k){
int r = lca(from, to);
int d1 = dep[from] - dep[r];
int d2 = dep[to] - dep[r];
if(d1 + d2 < k)return -1;
else if(k <= d1)return climb(from, k);
else return climb(to, d1 + d2 - k);
}
template<typename I>
Graph<T>lca_tree(vector<I>&v){
auto compare=[&](int x,int y){return in[x]<in[y];};
sort(v.begin(),v.end(),compare);
int sz1=v.size();
for(int i=0;i<sz1-1;i++)v.push_back(lca(v[i],v[i+1]));
sort(v.begin(),v.end(),compare);
v.erase(unique(v.begin(),v.end()),v.end());
int sz2=v.size();
Graph<T>ret(sz2);
stack<int>st;
for(int i=0;i<sz2;i++){
while(!st.empty()&&out[v[st.top()]]<=in[v[i]])st.pop();
if(!st.empty()){
ret[st.top()].emplace_back(i,dep[v[i]]-dep[v[st.top()]]);
ret[i].emplace_back(st.top(),dep[v[i]]-dep[v[st.top()]]);
}
st.push(i);
}
return ret;
}
};
const int VERTEX = 0;
const int HEAVY_LIGHT = -1;
const int LIGHT = -2;
const int HEAVY = -3;
template<typename T>
struct StaticToptree{
const HLD<T> &hld;
int count;
int root;
vector<int>l,r,p;
vector<int>aff;
T edge_identity;
StaticToptree(const HLD<T> &hld):hld(hld),edge_identity(edge_identity),count(hld.n),l(hld.n*2,-1),r(hld.n*2,-1),p(hld.n*2,-1),aff(hld.n*2,VERTEX){
int hld_root=min_element(hld.in.begin(),hld.in.end())-hld.in.begin();
root = dfs(hld_root,-1).second;
}
//sz,vid
pair<int,int>dfs(int v,int par){
int sub=0;
vector<int>vs;
vector<int>sz;
int now=v,pre=par;
while(1){
int sum_sz=1;
//vid,eid
priority_queue<pair<int,int>,vector<pair<int,int>>,greater<pair<int,int>>>pq;
for(int i=1;i<hld.g[now].size();i++){
if(hld.g[now][i].to==pre)continue;
auto [sz, vid] = dfs(hld.g[now][i].to, now);
pq.emplace(sz,vid);
sum_sz+=sz;
}
sub+=sum_sz;
while(pq.size()>=2){
auto [sx,x]=pq.top();pq.pop();
auto [sy,y]=pq.top();pq.pop();
int nv=count++;
aff[nv]=LIGHT;
l[nv]=x;
p[x]=nv;
r[nv]=y;
p[y]=nv;
pq.emplace(sx+sy,nv);
}
int last=now;
if(!pq.empty()){
auto [sx,x]=pq.top();pq.pop();
int nv=count++;
aff[nv]=HEAVY_LIGHT;
l[nv]=now;
p[x]=nv;
r[nv]=x;
p[now]=nv;
last=nv;
}
vs.push_back(last);
sz.push_back(sum_sz);
if(hld.g[now].empty()||hld.g[now][0]==pre)break;
pre=now;
now=hld.g[now][0];
}
vector<int>csz(sz.size()+1);
for(int i=0;i<sz.size();i++){
csz[i+1]=csz[i]+sz[i];
}
auto rec=[&](auto &&rec,int ls,int rs)->int{
{}
if(ls+1==rs){
return vs[ls];
}
int sum=csz[rs]-csz[ls];
int lv=-1,rv=-1;
if(sz[ls]*2>=sum){
lv=rec(rec,ls,ls+1);
rv=rec(rec,ls+1,rs);
}
else if(sz[rs-1]*2>=sum){
lv=rec(rec,ls,rs-1);
rv=rec(rec,rs-1,rs);
}
else{
int ri=min<int>(rs-1,lower_bound(csz.begin(),csz.end(),csz[ls]+(sum+1)/2)-csz.begin());
int li=max(ls+1,ri-1);
if(abs((csz[li]-csz[ls])*2-sum)<abs((csz[ri]-csz[ls])*2-sum)){
ri=li;
}
lv=rec(rec,ls,ri);
rv=rec(rec,ri,rs);
}
int nv=count++;
aff[nv]=HEAVY;
l[nv]=lv,p[lv]=nv;
r[nv]=rv,p[rv]=nv;
return nv;
};
int last=rec(rec,0,sz.size());
return make_pair(sub,last);
}
};
using cpx = complex<double>;
const double PI = acos(-1);
vector<cpx> roots = {{0, 0},
{1, 0}};
void ensure_capacity(int min_capacity) {
for (int len = roots.size(); len < min_capacity; len *= 2) {
for (int i = len >> 1; i < len; i++) {
roots.emplace_back(roots[i]);
double angle = 2 * PI * (2 * i + 1 - len) / (len * 2);
roots.emplace_back(cos(angle), sin(angle));
}
}
}
void fft(vector<cpx> &z, bool inverse) {
int n = z.size();
assert((n & (n - 1)) == 0);
ensure_capacity(n);
for (unsigned i = 1, j = 0; i < n; i++) {
int bit = n >> 1;
for (; j >= bit; bit >>= 1)
j -= bit;
j += bit;
if (i < j)
swap(z[i], z[j]);
}
for (int len = 1; len < n; len <<= 1) {
for (int i = 0; i < n; i += len * 2) {
for (int j = 0; j < len; j++) {
cpx root = inverse ? conj(roots[j + len]) : roots[j + len];
cpx u = z[i + j];
cpx v = z[i + j + len] * root;
z[i + j] = u + v;
z[i + j + len] = u - v;
}
}
}
if (inverse)
for (int i = 0; i < n; i++)
z[i] /= n;
}
vector<int> multiply_bigint(const vector<int> &a, const vector<int> &b, int base) {
int need = a.size() + b.size();
int n = 1;
while (n < need) n <<= 1;
vector<cpx> p(n);
for (size_t i = 0; i < n; i++) {
p[i] = cpx(i < a.size() ? a[i] : 0, i < b.size() ? b[i] : 0);
}
fft(p, false);
// a[w[k]] = (p[w[k]] + conj(p[w[n-k]])) / 2
// b[w[k]] = (p[w[k]] - conj(p[w[n-k]])) / (2*i)
vector<cpx> ab(n);
cpx r(0, -0.25);
for (int i = 0; i < n; i++) {
int j = (n - i) & (n - 1);
ab[i] = (p[i] * p[i] - conj(p[j] * p[j])) * r;
}
fft(ab, true);
vector<int> result(need);
long long carry = 0;
for (int i = 0; i < need; i++) {
long long d = (long long) (ab[i].real() + 0.5) + carry;
carry = d / base;
result[i] = d % base;
}
return result;
}
vector<int> multiply_mod(const vector<int> &a, const vector<int> &b, int m) {
int need = a.size() + b.size() - 1;
int n = 1;
while (n < need) n <<= 1;
vector<cpx> A(n);
for (size_t i = 0; i < a.size(); i++) {
int x = (a[i] % m + m) % m;
A[i] = cpx(x & ((1 << 15) - 1), x >> 15);
}
fft(A, false);
vector<cpx> B(n);
for (size_t i = 0; i < b.size(); i++) {
int x = (b[i] % m + m) % m;
B[i] = cpx(x & ((1 << 15) - 1), x >> 15);
}
fft(B, false);
vector<cpx> fa(n);
vector<cpx> fb(n);
for (int i = 0, j = 0; i < n; i++, j = n - i) {
cpx a1 = (A[i] + conj(A[j])) * cpx(0.5, 0);
cpx a2 = (A[i] - conj(A[j])) * cpx(0, -0.5);
cpx b1 = (B[i] + conj(B[j])) * cpx(0.5, 0);
cpx b2 = (B[i] - conj(B[j])) * cpx(0, -0.5);
fa[i] = a1 * b1 + a2 * b2 * cpx(0, 1);
fb[i] = a1 * b2 + a2 * b1;
}
fft(fa, true);
fft(fb, true);
vector<int> res(need);
for (int i = 0; i < need; i++) {
long long aa = (long long) (fa[i].real() + 0.5);
long long bb = (long long) (fb[i].real() + 0.5);
long long cc = (long long) (fa[i].imag() + 0.5);
res[i] = (aa % m + (bb % m << 15) + (cc % m << 30)) % m;
}
return res;
}
constexpr int digits(int base) noexcept {
return base <= 1 ? 0 : 1 + digits(base / 10);
}
constexpr int base = 1000'000'000;
constexpr int base_digits = digits(base);
constexpr int fft_base = 10'000; // fft_base^2 * n / fft_base_digits <= 10^15 for double
constexpr int fft_base_digits = digits(fft_base);
struct bigint {
// value == 0 is represented by empty z
vector<int> z; // digits
// sign == 1 <==> value >= 0
// sign == -1 <==> value < 0
int sign;
bigint(long long v = 0) {
*this = v;
}
bigint &operator=(long long v) {
sign = v < 0 ? -1 : 1;
v *= sign;
z.clear();
for (; v > 0; v = v / base)
z.push_back((int) (v % base));
return *this;
}
bigint(const string &s) {
read(s);
}
bigint &operator+=(const bigint &other) {
if (sign == other.sign) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
z[i] += carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] >= base;
if (carry)
z[i] -= base;
}
} else if (other != 0 /* prevent infinite loop */) {
*this -= -other;
}
return *this;
}
friend bigint operator+(bigint a, const bigint &b) {
a += b;
return a;
}
bigint &operator-=(const bigint &other) {
if (sign == other.sign) {
if ((sign == 1 && *this >= other) || (sign == -1 && *this <= other)) {
for (int i = 0, carry = 0; i < other.z.size() || carry; ++i) {
z[i] -= carry + (i < other.z.size() ? other.z[i] : 0);
carry = z[i] < 0;
if (carry)
z[i] += base;
}
trim();
} else {
*this = other - *this;
this->sign = -this->sign;
}
} else {
*this += -other;
}
return *this;
}
friend bigint operator-(bigint a, const bigint &b) {
a -= b;
return a;
}
bigint &operator*=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = 0, carry = 0; i < z.size() || carry; ++i) {
if (i == z.size())
z.push_back(0);
long long cur = (long long) z[i] * v + carry;
carry = (int) (cur / base);
z[i] = (int) (cur % base);
}
trim();
return *this;
}
bigint operator*(int v) const {
return bigint(*this) *= v;
}
friend pair<bigint, bigint> divmod(const bigint &a1, const bigint &b1) {
int norm = base / (b1.z.back() + 1);
bigint a = a1.abs() * norm;
bigint b = b1.abs() * norm;
bigint q, r;
q.z.resize(a.z.size());
for (int i = (int) a.z.size() - 1; i >= 0; i--) {
r *= base;
r += a.z[i];
int s1 = b.z.size() < r.z.size() ? r.z[b.z.size()] : 0;
int s2 = b.z.size() - 1 < r.z.size() ? r.z[b.z.size() - 1] : 0;
int d = (int) (((long long) s1 * base + s2) / b.z.back());
r -= b * d;
while (r < 0)
r += b, --d;
q.z[i] = d;
}
q.sign = a1.sign * b1.sign;
r.sign = a1.sign;
q.trim();
r.trim();
return {q, r / norm};
}
friend bigint sqrt(const bigint &a1) {
bigint a = a1;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
int n = a.z.size();
int firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
int norm = base / (firstDigit + 1);
a *= norm;
a *= norm;
while (a.z.empty() || a.z.size() % 2 == 1)
a.z.push_back(0);
bigint r = (long long) a.z[n - 1] * base + a.z[n - 2];
firstDigit = (int) ::sqrt((double) a.z[n - 1] * base + a.z[n - 2]);
int q = firstDigit;
bigint res;
for (int j = n / 2 - 1; j >= 0; j--) {
for (;; --q) {
bigint r1 = (r - (res * 2 * base + q) * q) * base * base +
(j > 0 ? (long long) a.z[2 * j - 1] * base + a.z[2 * j - 2] : 0);
if (r1 >= 0) {
r = r1;
break;
}
}
res *= base;
res += q;
if (j > 0) {
int d1 = res.z.size() + 2 < r.z.size() ? r.z[res.z.size() + 2] : 0;
int d2 = res.z.size() + 1 < r.z.size() ? r.z[res.z.size() + 1] : 0;
int d3 = res.z.size() < r.z.size() ? r.z[res.z.size()] : 0;
q = (int) (((long long) d1 * base * base + (long long) d2 * base + d3) / (firstDigit * 2));
}
}
res.trim();
return res / norm;
}
bigint operator/(const bigint &v) const {
return divmod(*this, v).first;
}
bigint operator%(const bigint &v) const {
return divmod(*this, v).second;
}
bigint &operator/=(int v) {
if (v < 0)
sign = -sign, v = -v;
for (int i = (int) z.size() - 1, rem = 0; i >= 0; --i) {
long long cur = z[i] + rem * (long long) base;
z[i] = (int) (cur / v);
rem = (int) (cur % v);
}
trim();
return *this;
}
bigint operator/(int v) const {
return bigint(*this) /= v;
}
int operator%(int v) const {
if (v < 0)
v = -v;
int m = 0;
for (int i = (int) z.size() - 1; i >= 0; --i)
m = (int) ((z[i] + m * (long long) base) % v);
return m * sign;
}
bigint &operator*=(const bigint &v) {
*this = *this * v;
return *this;
}
bigint &operator/=(const bigint &v) {
*this = *this / v;
return *this;
}
bigint &operator%=(const bigint &v) {
*this = *this % v;
return *this;
}
bool operator<(const bigint &v) const {
if (sign != v.sign)
return sign < v.sign;
if (z.size() != v.z.size())
return z.size() * sign < v.z.size() * v.sign;
for (int i = (int) z.size() - 1; i >= 0; i--)
if (z[i] != v.z[i])
return z[i] * sign < v.z[i] * sign;
return false;
}
bool operator>(const bigint &v) const {
return v < *this;
}
bool operator<=(const bigint &v) const {
return !(v < *this);
}
bool operator>=(const bigint &v) const {
return !(*this < v);
}
bool operator==(const bigint &v) const {
return !(*this < v) && !(v < *this);
}
bool operator!=(const bigint &v) const {
return *this < v || v < *this;
}
void trim() {
while (!z.empty() && z.back() == 0)
z.pop_back();
if (z.empty())
sign = 1;
}
bool isZero() const {
return z.empty();
}
friend bigint operator-(bigint v) {
if (!v.z.empty())
v.sign = -v.sign;
return v;
}
bigint abs() const {
return sign == 1 ? *this : -*this;
}
long long longValue() const {
long long res = 0;
for (int i = (int) z.size() - 1; i >= 0; i--)
res = res * base + z[i];
return res * sign;
}
friend bigint gcd(const bigint &a, const bigint &b) {
return b.isZero() ? a : gcd(b, a % b);
}
friend bigint lcm(const bigint &a, const bigint &b) {
return a / gcd(a, b) * b;
}
void read(const string &s) {
sign = 1;
z.clear();
int pos = 0;
while (pos < s.size() && (s[pos] == '-' || s[pos] == '+')) {
if (s[pos] == '-')
sign = -sign;
++pos;
}
for (int i = (int) s.size() - 1; i >= pos; i -= base_digits) {
int x = 0;
for (int j = max(pos, i - base_digits + 1); j <= i; j++)
x = x * 10 + s[j] - '0';
z.push_back(x);
}
trim();
}
friend istream &operator>>(istream &stream, bigint &v) {
string s;
stream >> s;
v.read(s);
return stream;
}
friend ostream &operator<<(ostream &stream, const bigint &v) {
if (v.sign == -1)
stream << '-';
stream << (v.z.empty() ? 0 : v.z.back());
for (int i = (int) v.z.size() - 2; i >= 0; --i)
stream << setw(base_digits) << setfill('0') << v.z[i];
return stream;
}
static vector<int> convert_base(const vector<int> &a, int old_digits, int new_digits) {
vector<long long> p(max(old_digits, new_digits) + 1);
p[0] = 1;
for (int i = 1; i < p.size(); i++)
p[i] = p[i - 1] * 10;
vector<int> res;
long long cur = 0;
int cur_digits = 0;
for (int v : a) {
cur += v * p[cur_digits];
cur_digits += old_digits;
while (cur_digits >= new_digits) {
res.push_back(int(cur % p[new_digits]));
cur /= p[new_digits];
cur_digits -= new_digits;
}
}
res.push_back((int) cur);
while (!res.empty() && res.back() == 0)
res.pop_back();
return res;
}
bigint operator*(const bigint &v) const {
if (min(z.size(), v.z.size()) < 150)
return mul_simple(v);
bigint res;
res.sign = sign * v.sign;
res.z = multiply_bigint(convert_base(z, base_digits, fft_base_digits),
convert_base(v.z, base_digits, fft_base_digits), fft_base);
res.z = convert_base(res.z, fft_base_digits, base_digits);
res.trim();
return res;
}
bigint mul_simple(const bigint &v) const {
bigint res;
res.sign = sign * v.sign;
res.z.resize(z.size() + v.z.size());
for (int i = 0; i < z.size(); ++i)
if (z[i])
for (int j = 0, carry = 0; j < v.z.size() || carry; ++j) {
long long cur = res.z[i + j] + (long long) z[i] * (j < v.z.size() ? v.z[j] : 0) + carry;
carry = (int) (cur / base);
res.z[i + j] = (int) (cur % base);
}
res.trim();
return res;
}
};
mt19937 rng(1);
bigint random_bigint(int n) {
string s;
for (int i = 0; i < n; i++) {
s += uniform_int_distribution<int>('0', '9')(rng);
}
return bigint(s);
}
vector<string>val;
Graph<int>tree;
using State = string::iterator;
template<typename T>
struct Parsing{
Parsing(){};
T solve(string &s){
State itr = s.begin();
return expr(itr);
}
T expr(State &itr){
T now = term(itr);
while(1){
if(*itr == '+' || *itr == '-'){
char sig=*itr;
T nxt = term(++itr);
int idx=tree.size();
tree.EB();
tree[idx].EB(now);
tree[idx].EB(nxt);
val.PB(string(1,sig));
now=idx;
}
else break;
}
return now;
}
T term(State &itr){
T now = fact(itr);
while(1){
if(*itr == '*'){
T nxt = fact(++itr);
int idx = tree.size();
tree.emplace_back();
tree[idx].emplace_back(now);
tree[idx].emplace_back(nxt);
val.PB("*");
now=idx;
}
else break;
}
return now;
}
T fact(State &itr){
if(*itr=='-'||isdigit(*itr))return number(itr);
assert(*itr == '(');
itr++;
T val = expr(itr);
assert(*itr == ')');
itr++;
return val;
}
T number(State &itr){
string num;
while(*itr=='-'){
num += *itr;
itr++;
}
while(isdigit(*itr)){
num += *itr;
itr++;
}
int idx=tree.size();
tree.emplace_back();
val.push_back(num);
return idx;
}
};
int main(){
cin.tie(nullptr);
ios_base::sync_with_stdio(false);
ll res=0,buf=0;
bool judge = true;
ll n;cin>>n;
string s;cin>>s;
Parsing<int>parse;
int root=parse.solve(s);
OUT(tree,val);
return 0;
}