#include <bits/stdc++.h>
#include "meetings.h"
using namespace std;
struct segment_tree{
vector<int> st, v;
int maxn;
int get(int x, int y){
if(x == maxn) return y;
if(y == maxn) return x;
return v[x] >= v[y] ? x : y;
}
void init(vector<int> ert, int n){
maxn = n;
while(maxn != (maxn&(-maxn))) maxn += (maxn&(-maxn));
v = ert;
st.resize(maxn<<1, maxn);
iota(st.begin()+maxn, st.begin()+maxn+n, 0);
for(int i = maxn-1; i > 0; i--)
st[i] = get(st[2*i], st[2*i+1]);
}
int query(int s, int e, int x, int l, int r){
if(e <= l || r <= s)
return maxn;
if(s <= l && r <= e)
return st[x];
int m = (l+r)/2;
return get(query(s, e, 2*x, l, m), query(s, e, 2*x+1, m, r));
}
int query(int l, int r){
return query(l, r, 1, 0, maxn);
}
};
struct node{
int l, r, lc, rc;
long long ert;
node *L = nullptr, *R = nullptr;
node(){}
node(node *L, node *R, int l, int r, int lc, int rc) : L(L), R(R), l(l), r(r), lc(lc), rc(rc) {};
};
typedef node* gnode;
struct st_adat{
long long ossz, ert, hl, hr, len;
};
struct adat{
int ind, l, r;
};
const long long INF = (long long)1e18;
segment_tree maxST;
vector<int> h;
gnode build(int l, int r, int lc, int rc){
if(l+1 == r){
gnode temp = new node(nullptr, nullptr, l, r, lc, rc);
temp->ert = h[l];
return temp;
}
int m = maxST.query(l, r);
int c = h[m];
if(m == l) m++;
gnode p = new node(build(l, m, lc, c), build(m, r, c, rc), l, r, lc, rc);
p->ert = min(p->L->ert + (long long)(r-m)*c, p->R->ert + (long long)(m-l)*c);
return p;
}
const int stn = 1<<20;
st_adat st[stn<<1];
void kiir(gnode p){
cout<<"node: ("<<(p->l)<<", "<<(p->r)<<") ert: "<<p->ert<<" cl: "<<p->lc<<" cr: "<<p->rc<<"\n";
}
void kiir(st_adat d){
cout<<"st_adat: "<<d.ossz<<" "<<d.ert<<" "<<d.hl<<" "<<d.hr<<" "<<d.len<<"\n";
}
st_adat get(st_adat ld, st_adat rd){
if(ld.ossz == INF) return rd;
if(rd.ossz == INF) return ld;
return {ld.ossz + rd.ossz, min(ld.ert + rd.len*ld.hr, rd.ert + ld.ossz), ld.hl, rd.hr, ld.len+rd.len};
}
void add(int x, st_adat d){
st[x+stn] = d;
//cout<<"add: ";
//kiir(d);
for(int i = (x+stn)>>1; i > 0; i >>= 1)
st[i] = get(st[2*i], st[2*i+1]);
}
st_adat query(int s, int e, int x, int l, int r){
if(r <= s || e <= l)
return {INF};
if(s <= l && r <= e){
//cout<<"\n";
//cout<<"st query: "<<l<<" "<<r<<" "<<x<<"\n";
//kiir(st[x]);
//cout<<"\n";
return st[x];
}
int m = (l+r)/2;
return get(query(s, e, 2*x, l, m), query(s, e, 2*x+1, m, r));
}
vector<vector<adat>> vegek((int)1e6);
vector<long long> meg;
int starts[(int)1e6];
void add_node(gnode p, int ind){
starts[ind] = p->l;
long long ossz = (long long)(p->r-p->l)*p->rc;
if(h[p->l] > p->rc) ossz += (long long)(h[p->l] - p->rc);
//cout<<"add from node: ";
//kiir(p);
add(ind, {ossz, p->ert, p->lc, p->rc, p->r-p->l});
}
void bejar(gnode p, int len){
//kiir(p);
if(p->l+1 == p->r){
/*cout<<"Ind: "<<p->l<<" "<<vegek[p->l].size()<<" "<<len<<"\n";
for(int i = 0; i < len; i++)
cout<<starts[i]<<" ";
cout<<" sor\n";*/
for(adat d : vegek[p->l]){
int m = lower_bound(starts, starts+len, d.l)-starts;
if(m == len) continue;
//cout<<m<<" "<<starts[m]<<" "<<len<<" check\n";
st_adat x = query(m, len, 1, 0, stn);
//kiir(x);
meg[d.ind] = min(meg[d.ind], x.ert + x.hl*(starts[m]-d.l));
}
return;
}
bejar(p->L, len);
add_node(p->L, len);
bejar(p->R, len+1);
}
std::vector<long long> minimum_costs(std::vector<int> H, std::vector<int> L, std::vector<int> R) {
H.push_back((int)1e9+1);
H.insert(H.begin(), (int)1e9+1);
int n = (int)H.size();
int q = (int)L.size();
h = H;
meg.resize(q, INF);
maxST.init(H, n);
for(int i = 0; i < q; i++)
vegek[R[i]+2].push_back({i, L[i]+1, R[i]+1});
bejar(build(0, n, 0, 0), 0);
for(int i = 0; i < q; i++)
vegek[R[i]+2].clear();
reverse(h.begin(), h.end());
maxST.init(h, n);
for(int i = 0; i < q; i++)
vegek[n-L[i]-1].push_back({i, n-R[i]-2, n-L[i]-2});
bejar(build(0, n, 0, 0), 0);
return meg;
}
