#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef double ld;
typedef complex<ld> point;
void debug_out(){cerr << endl;}
template<typename Head, typename... Tail>
void debug_out(Head H, Tail... T){
cerr << H << ' ';
debug_out(T...);
}
#define debug(...) cerr << "(" << #__VA_ARGS__ << "): ", debug_out(__VA_ARGS__)
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define MP(x, y) make_pair(x, y)
const int maxn = 1e6 + 10;
struct Seg{
ll l, r;
};
pll lazy1[maxn << 2];
ll lazy2[maxn << 2];
Seg seg[maxn << 2];
Seg operator +(Seg a, Seg b){
Seg res;
res.l = a.l;
res.r = b.r;
return res;
}
void shift(int v, int l, int r);
void change(int v, int l, int r, int ql, int qr, ll a, ll b){
// if (v == 1) debug(ql, qr, a, b);
if (qr <= l || r <= ql) return;
if (!(ql <= l && r <= qr)){
shift(v, l, r);
int mid = (l + r) >> 1;
change(v << 1, l, mid, ql, qr, a, b);
change(v << 1 | 1, mid, r, ql, qr, a, b);
}
else{
// debug(v, l, r, ql, qr, a, b, seg[v].l, seg[v].r);
if (a + b * l <= seg[v].l && a + b * (r-1) <= seg[v].r){
seg[v].l = a + b * l;
seg[v].r = a + b * (r-1);
lazy1[v] = {a, b};
// debug(seg[v].l, seg[v].r, seg[v].mx, lazy1[v].F, lazy1[v].S);
return;
}
if (a + b * l > seg[v].l && a + b * (r-1) > seg[v].r) return;
shift(v, l, r);
int mid = (l + r) >> 1;
change(v << 1, l, mid, ql, qr, a, b);
change(v << 1 | 1, mid, r, ql, qr, a, b);
}
seg[v] = seg[v << 1] + seg[v << 1 | 1];
}
void add(int v, int l, int r, int ql, int qr, ll val){
//if (v == 1) debug(ql, qr, val);
if (qr <= l || r <= ql) return;
if (ql <= l && r <= qr){
// debug(v, l, r, ql, qr, val);
seg[v].l += val;
seg[v].r += val;
lazy1[v].F += val;
lazy2[v] += val;
return;
}
shift(v, l, r);
int mid = (l + r) >> 1;
add(v << 1, l, mid, ql, qr, val);
add(v << 1 | 1, mid, r, ql, qr, val);
seg[v] = seg[v << 1] + seg[v << 1 | 1];
}
ll get(int v, int l, int r, int idx){
//if (v == 1) debug(idx);
if (l + 1 == r) return seg[v].l;
shift(v, l, r);
int mid = (l + r) >> 1;
if (idx < mid) return get(v << 1, l, mid, idx);
else return get(v << 1 | 1, mid, r, idx);
}
void shift(int v, int l, int r){
if (lazy2[v] == 0 && lazy1[v].S == -1) return;
int mid = (l + r) >> 1;
if (lazy2[v] != 0){
add(v << 1, l, mid, l, mid, lazy2[v]);
add(v << 1 | 1, mid, r, mid, r, lazy2[v]);
}
if (lazy1[v].S != -1){
change(v << 1, l, mid, l, mid, lazy1[v].F, lazy1[v].S);
change(v << 1 | 1, mid, r, mid, r, lazy1[v].F, lazy1[v].S);
}
lazy1[v] = {0, -1};
lazy2[v] = 0;
}
const int lg = 20;
const ll inf = 1e18;
int n, q, h[maxn], queryl[maxn], queryr[maxn];
ll ans[maxn];
pii rmq[lg][maxn];
vector<pair<pii,int>> Q[maxn];
pii getmx(int l, int r){
r++;
int x = 31 - __builtin_clz(r-l);
return max(rmq[x][l], rmq[x][r-(1<<x)]);
}
void solve(bool flg){
vector<pii> val;
for (int i = 0; i < n; i++){
Q[i].clear();
}
for (int i = 1; i < 4*maxn; i++){
seg[i] = {0, 0};
lazy1[i] = {0, -1};
lazy2[i] = 0;
}
for (int i = 0; i < n; i++){
if (!flg){
val.push_back({h[i], i});
rmq[0][i] = {h[i], i};
}
else{
val.push_back({h[i], -i});
rmq[0][i] = {h[i], -i};
}
}
for (int i = 1; i < lg; i++){
for (int j = 0; j + (1 << i) <= n; j++){
rmq[i][j] = max(rmq[i-1][j], rmq[i-1][j+(1<<(i-1))]);
}
}
for (int i = 0; i < q; i++){
int mx = abs(getmx(queryl[i], queryr[i]).S);
Q[mx].push_back({{queryl[i], queryr[i]}, i});
}
sort(all(val));
for (auto [x, y]: val){
y = abs(y);
// debug(x, y);
for (auto [tmp, idx]: Q[y]){
ans[idx] = min(ans[idx], get(1, 0, n, tmp.S) + 1ll * (y-tmp.F+1) * x);
}
int l = -1, r = y;
while(l + 1 < r){
int mid = (l + r) >> 1;
if (abs(getmx(mid, y).S) == y) r = mid;
else l = mid;
}
int l2 = y, r2 = n;
while(l2 + 1 < r2){
int mid = (l2 + r2) >> 1;
if (abs(getmx(y, mid).S) == y) l2 = mid;
else r2 = mid;
}
add(1, 0, n, y, r2, 1ll * (y-l) * x);
if (r == y) continue;
ll tmp = get(1, 0, n, y-1);
tmp -= 1ll * (y-1) * x;
change(1, 0, n, y, r2, tmp, x);
}
}
vector<ll> minimum_costs(vector<int> H, vector<int> L, vector<int> R) {
n = H.size();
q = L.size();
for (int i = 0; i < n; i++){
h[i] = H[i];
}
for (int i = 0; i < q; i++){
queryl[i] = L[i];
queryr[i] = R[i];
ans[i] = inf;
}
solve(false);
// debug("----------------");
// for (int i = 0; i < q; i++) debug(i, ans[i]);
for (int i = 0; i < q; i++){
queryl[i] = n-R[i]-1;
queryr[i] = n-L[i]-1;
}
for (int i = 0; i < n/2; i++){
swap(h[i], h[n-i-1]);
}
solve(true);
vector<ll> res;
for (int i = 0; i < q; i++) res.push_back(ans[i]);
return res;
}
