#define DEBUG 0
#include <bits/stdc++.h>
using namespace std;
#if DEBUG
// basic debugging macros
int __i__,__j__;
#define printLine(l) for(__i__=0;__i__<l;__i__++){cout<<"-";}cout<<endl
#define printLine2(l,c) for(__i__=0;__i__<l;__i__++){cout<<c;}cout<<endl
#define printVar(n) cout<<#n<<": "<<n<<endl
#define printArr(a,l) cout<<#a<<": ";for(__i__=0;__i__<l;__i__++){cout<<a[__i__]<<" ";}cout<<endl
#define print2dArr(a,r,c) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<a[__i__][__j__]<<" ";}cout<<endl;}
#define print2dArr2(a,r,c,l) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<setw(l)<<setfill(' ')<<a[__i__][__j__]<<" ";}cout<<endl;}
// advanced debugging class
// debug 1,2,'A',"test";
class _Debug {
public:
template<typename T>
_Debug& operator,(T val) {
cout << val << endl;
return *this;
}
};
#define debug _Debug(),
#else
#define printLine(l)
#define printLine2(l,c)
#define printVar(n)
#define printArr(a,l)
#define print2dArr(a,r,c)
#define print2dArr2(a,r,c,l)
#define debug
#endif
// define
#define MAX_VAL 999999999
#define MAX_VAL_2 999999999999999999LL
#define EPS 1e-6
#define mp make_pair
#define pb push_back
// typedef
typedef unsigned int UI;
typedef long long int LLI;
typedef unsigned long long int ULLI;
typedef unsigned short int US;
typedef pair<int,int> pii;
typedef pair<LLI,LLI> plli;
typedef vector<int> vi;
typedef vector<LLI> vlli;
typedef vector<pii> vpii;
typedef vector<plli> vplli;
// ---------- END OF TEMPLATE ----------
#include "meetings.h"
#pragma GCC optimize("Ofast")
int N,h[750000],sparse[750000][20];
int logg[750001];
int rev = 0;
int query(int s,int e) {
if (rev) {
s = N-1-s,e = N-1-e,swap(s,e);
int l = logg[e-s+1];
return (h[N-sparse[s][l]-1] > h[N-sparse[e-(1 << l)+1][l]-1]) ? N-sparse[s][l]-1:N-sparse[e-(1 << l)+1][l]-1;
}
else {
int l = logg[e-s+1];
return (h[sparse[s][l]] > h[sparse[e-(1 << l)+1][l]]) ? sparse[s][l]:sparse[e-(1 << l)+1][l];
}
}
vector<pair<pii,int> > qq[750000];
LLI ans[750000];
LLI tree[1 << 21],lazyb[1 << 21];
int lazym[1 << 21],lazy[1 << 21];
int build(int s,int e,int i) {
if (s == e) {
tree[i] = lazym[i] = lazyb[i] = lazy[i] = 0;
return 0;
}
int mid = (s+e) / 2;
build(s,mid,2*i+1),build(mid+1,e,2*i+2);
tree[i] = lazym[i] = lazyb[i] = lazy[i] = 0;
return 0;
}
int prop(int s,int e,int i) {
if (lazy[i]) {
tree[i] = (LLI) lazym[i]*(e-s)+lazyb[i];
if (s != e) {
int mid = (s+e) / 2;
lazym[2*i+1] = lazym[2*i+2] = lazym[i];
lazyb[2*i+1] = lazyb[i],lazyb[2*i+2] = (LLI) lazym[i]*(mid+1-s)+lazyb[i];
lazy[2*i+1] = lazy[2*i+2] = 1;
}
lazy[i] = lazym[i] = lazyb[i] = 0;
}
else if (lazyb[i] != 0) {
tree[i] += lazyb[i];
if (s != e) lazyb[2*i+1] += lazyb[i],lazyb[2*i+2] += lazyb[i];
lazyb[i] = 0;
}
return 0;
}
int update(int s,int e,int as,int ae,int i,int m,LLI b,int t) {
prop(s,e,i);
if ((s > ae) || (e < as)) return 0;
else if ((s >= as) && (e <= ae)) {
lazy[i] = t,lazym[i] = m,lazyb[i] = (LLI) m*(s-as)+b;
prop(s,e,i);
return 0;
}
int mid = (s+e) / 2;
if (as <= mid) update(s,mid,as,ae,2*i+1,m,b,t);
update(mid+1,e,as,ae,2*i+2,m,b,t);
tree[i] = tree[2*i+2];
return 0;
}
LLI query(int s,int e,int q,int i) {
if (lazy[i]) return lazyb[i]+(LLI) lazym[i]*(q-s);
prop(s,e,i);
if (q == e) return tree[i];
int mid = (s+e) / 2;
if (q <= mid) return query(s,mid,q,2*i+1);
else return query(mid+1,e,q,2*i+2);
}
int query2(int s,int e,int qs,int qe,int i,LLI q) {
prop(s,e,i);
if ((s > qe) || (e < qs)) return -1;
else if ((e <= qe) && (tree[i] < q+(LLI) h[qe]*(qe-e+1))) return -1;
else if ((s >= qs) && (e <= qe)) {
while (s != e) {
int mid = (s+e) / 2;
prop(s,mid,2*i+1);
if (tree[2*i+1] >= q+(LLI) h[qe]*(qe-mid+1)) e = mid,i = 2*i+1;
else prop(mid+1,e,2*i+2),s = mid+1,i = 2*i+2;
}
return s;
}
int mid = (s+e) / 2;
int r = query2(s,mid,qs,qe,2*i+1,q);
if (r != -1) return r;
else return query2(mid+1,e,qs,qe,2*i+2,q);
}
LLI solve(int s,int e) {
if (s > e) return 0;
int i;
int m = query(s,e);
LLI a = solve(s,m-1),b = solve(m+1,e);
for (i = 0; i < qq[m].size(); i++) {
if ((LLI) h[m]*(qq[m][i].first.second-m+1) >= ans[qq[m][i].second]) continue;
LLI q = (qq[m][i].first.first == m) ? 0:((qq[m][i].first.first == s) ? a:query(0,N-1,qq[m][i].first.first,0));
ans[qq[m][i].second] = min(ans[qq[m][i].second],q+(LLI) h[m]*(qq[m][i].first.second-m+1));
}
qq[m].clear();
int pos;
a += (LLI) h[m]*(e-m+1);
if (a < b+(LLI) h[m]*(m-s+1)) {
pos = (h[m-1]+(LLI) h[m]*(e-m+1) < b+(LLI) h[m]*2) ? m:query2(0,N-1,s,m,0,b-(LLI) h[m]*(e-m+1));
update(0,N-1,s,pos-1,0,0,(LLI) h[m]*(e-m+1),0);
}
else a = b+(LLI) h[m]*(m-s+1),pos = s;
update(0,N-1,pos,m,0,-h[m],b+(LLI) h[m]*(m-pos+1),1);
return a;
}
vector<long long int> minimum_costs(vector<int> H,vector<int> L,vector<int> R) {
int i,j,Q = L.size();
N = H.size();
for (i = 0; i < N; i++) h[i] = H[i],sparse[i][0] = i;
for (i = 1; (1 << i) <= N; i++) {
for (j = 0; j <= N-(1 << i); j++) sparse[j][i] = (h[sparse[j][i-1]] > h[sparse[j+(1 << (i-1))][i-1]]) ? sparse[j][i-1]:sparse[j+(1 << (i-1))][i-1];
}
for (i = 2; i <= N; i++) logg[i] = logg[i/2]+1;
for (i = 0; i < Q; i++) {
int q = query(L[i],R[i]);
qq[q].pb(mp(mp(L[i],R[i]),i));
ans[i] = 1e18;
}
solve(0,N-1),reverse(h,h+N),rev = 1;
for (i = 0; i < Q; i++) {
L[i] = N-L[i]-1,R[i] = N-R[i]-1,swap(L[i],R[i]);
int q = query(L[i],R[i]);
qq[q].pb(mp(mp(L[i],R[i]),i));
}
build(0,N-1,0),solve(0,N-1);
return vector<LLI>(ans,ans+Q);
}
