#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
#define FOR(i, a, b) for (int i=a; i<(b); i++)
#define F0R(i, a) for (int i=0; i<(a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= a; i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define sz(x) (int)(x).size()
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
const int MOD = 1000000007;
const ll INF = 1e18;
const int MX = 1<<20;
const int SZ = 750001;
#include "meetings.h"
pl operator*(const pl& l, const ll& r) { return {l.f*r,l.s*r}; }
pl operator+(const pl& l, const pl& r) { return {l.f+r.f,l.s+r.s}; }
pl operator+=(pl& l, const pl& r) { return l = {l.f+r.f,l.s+r.s}; }
int N;
vpi hei;
void checkmn(ll& x, ll y) { x = min(x,y); }
struct RMQ {
int mx[21][SZ];
int bet(int a, int b) {
return hei[a] > hei[b] ? a : b;
}
void clear() {
F0R(i,N) mx[0][i] = i;
FOR(j,1,21) F0R(i,N-(1<<j)+1)
mx[j][i] = bet(mx[j-1][i],mx[j-1][i+(1<<(j-1))]);
}
int query(int L, int R) {
int x = 31-__builtin_clz(R-L+1);
return bet(mx[x][L],mx[x][R-(1<<x)+1]);
}
};
RMQ RM;
struct DSU {
int par[SZ], left[SZ], right[SZ];
void clear() {
F0R(i,SZ) par[i] = left[i] = right[i] = i;
}
int get(int x) {
if (par[x] != x) return par[x] = get(par[x]);
return x;
}
inline void unite(int a, int b) {
a = get(a), b = get(b);
if (right[a]-left[a] < right[b]-left[b]) swap(a,b);
par[b] = a;
left[a] = min(left[a],left[b]);
right[a] = max(right[a],right[b]);
}
};
ll ans[SZ];
vector<array<int,3>> tmp[SZ];
struct Seg {
ll val[2*MX];
pair<int,pl> lazy[2*MX], done = mp(1,mp(0,0));
inline void push(int ind, int L, int R) {
if (lazy[ind] == done) return;
val[ind] = val[ind]*lazy[ind].f+lazy[ind].s.f*R+lazy[ind].s.s;
if (L != R) {
if (lazy[ind].f == 0) lazy[2*ind] = lazy[ind];
else lazy[2*ind].s += lazy[ind].s;
if (lazy[ind].f == 0) lazy[2*ind+1] = lazy[ind];
else lazy[2*ind+1].s += lazy[ind].s;
}
lazy[ind] = done;
}
inline void pull(int ind) { val[ind] = val[2*ind+1]; }
void upd(int lo, int hi, pair<int,pl> A, int ind = 1, int L = 0, int R = SZ-1) {
push(ind,L,R);
if (R < lo || hi < L) return;
if (lo <= L && R <= hi) {
lazy[ind] = A;
push(ind,L,R);
return;
}
int M = (L+R)/2;
upd(lo,hi,A,2*ind,L,M); upd(lo,hi,A,2*ind+1,M+1,R);
pull(ind);
}
ll get(int pos, int ind = 1, int L = 0, int R = SZ-1) {
push(ind,L,R);
if (L == R) return val[ind];
int M = (L+R)/2;
if (pos <= M) return get(pos,2*ind,L,M);
return get(pos,2*ind+1,M+1,R);
}
int getFst(int x, int lo, int hi, ll ori, int ind = 1, int L = 0, int R = SZ-1) {
push(ind,L,R);
int M = (L+R)/2;
if (R <= hi) {
if (R <= x) return -1;
ll val1 = (ll)hei[x].f*(R-x+1)+ori;
ll val2 = (ll)hei[x].f*(x-lo+1)+val[ind]; // first one such that 2nd is less
if (val1 < val2) return -1;
}
if (L == R) return L;
int z = getFst(x,lo,hi,ori,2*ind,L,M); if (z != -1) return z;
return getFst(x,lo,hi,ori,2*ind+1,M+1,R);
}
};
Seg S;
DSU D;
void tri(int x) {
if (x < N-1 && hei[x] > hei[x+1]) D.unite(x,x+1);
if (x > 0 && hei[x] > hei[x-1]) D.unite(x-1,x);
int L = D.left[D.get(x)], R = D.right[D.get(x)];
ll preVal = (L == x ? 0 : S.get(x-1));
for (auto y: tmp[x]) checkmn(ans[y[2]],(ll)(x-y[0]+1)*hei[x].f+S.get(y[1]));
int ind = S.getFst(x,L,R,preVal); if (ind == -1) ind = R+1;
S.upd(x,ind-1,{0,{hei[x].f,preVal-(ll)(x-1)*hei[x].f}});
S.upd(ind,R,{1,{0,(ll)(x-L+1)*hei[x].f}});
}
void solve(vi L, vi R) {
RM.clear();
D.clear();
S = Seg();
vi h; F0R(i,N) h.pb(i);
sort(all(h),[](int a, int b) { return hei[a] < hei[b]; });
F0R(i,SZ) tmp[i].clear();
F0R(i,sz(L)) tmp[RM.query(L[i],R[i])].pb({L[i],R[i],i});
F0R(i,sz(h)) tri(h[i]);
}
std::vector<long long> minimum_costs(std::vector<int> H, std::vector<int> L,
std::vector<int> R) {
N = sz(H);
F0R(i,N) hei.pb({H[i],i});
F0R(i,sz(L)) ans[i] = INF;
solve(L,R);
reverse(all(hei));
F0R(i,sz(L)) {
L[i] = sz(H)-1-L[i];
R[i] = sz(H)-1-R[i];
swap(L[i],R[i]);
}
solve(L,R);
vl ret; F0R(i,sz(L)) ret.pb(ans[i]);
return ret;
}
