#include "meetings.h"
#include <bits/stdc++.h>
#define rep(i, n) for (ll i = 0; i < ll(n); ++i)
#define rep2(i, s, n) for (ll i = ll(s); i < ll(n); ++i)
#define rrep(i, n) for (ll i = ll(n)-1; i >= 0; --i)
#define pb push_back
#define eb emplace_back
#define all(a) a.begin(),a.end()
#define SZ(a) int(a.size())
using namespace std;
using ll = long long;
using P = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using vp = vector<P>;
using vvp = vector<vp>;
using vb = vector<bool>;
using vvb = vector<vb>;
using vs = vector<string>;
const int inf = 1001001001;
const ll linf = 1001001001001001001;
template<class T>
bool chmin(T &a, T b) {
if (a > b) {
a = b;
return true;
}
return false;
}
template<class T>
bool chmax(T &a, T b) {
if (a < b) {
a = b;
return true;
}
return false;
}
struct line {
ll a, b;
line(ll _a, ll _b) : a(_a), b(_b) {}
ll eval(ll x) { return a * x + b; }
};
class LCT {
int n;
vi lb, ub;
vector<line> v;
public:
LCT(int _n) {
n = 1;
while (n < _n) n *= 2;
v.assign(2 * n, line(0, linf));
lb.resize(2 * n);
ub.resize(2 * n);
rep(i, n) {
lb[n + i] = i;
ub[n + i] = i + 1;
}
for (int i = n - 1; i >= 1; --i) {
lb[i] = lb[2 * i];
ub[i] = ub[2 * i + 1];
}
}
ll get_min(int p) {
assert(0 <= p and p < n);
ll mn = linf;
int it = p + n;
while (it >= 1) {
chmin(mn, v[it].eval(p));
it >>= 1;
}
return mn;
}
void add_line(int k, line now) {
int l = lb[k], r = ub[k];
int m = (l + r) / 2;
bool wl = v[k].eval(l) > now.eval(l);
bool wm = v[k].eval(m) > now.eval(m);
bool wr = v[k].eval(r) > now.eval(r);
if (r - l == 1) {
if (wl) v[k] = now;
return;
}
if (wl and wr) {
v[k] = now;
return;
}
if (!wl and !wr) return;
if (wm) {
swap(v[k], now);
wl = !wl;
wr = !wr;
}
if (wl) add_line(2 * k, now);
else add_line(2 * k + 1, now);
}
void add_segment(int l, int r, line now) {
assert(0 <= l and l <= r and r <= n);
l += n, r += n;
while (l < r) {
if (l & 1) add_line(l++, now);
if (r & 1) add_line(--r, now);
l >>= 1, r >>= 1;
}
}
};
vl minimum_costs(vi h, vi l, vi r) {
int n = SZ(h);
int q = SZ(l);
for (int &i: r) ++i;
vl ans(q, linf);
rep(_, 2) {
vl v(n);
vi st;
vi lim(n);
rrep(i, n) {
vi tmp;
while (not st.empty() and h[st.back()] < h[i]) {
int j = st.back();
st.pop_back();
tmp.pb(j);
lim[j] = i + 1;
}
int ub = (st.empty() ? n : st.back());
st.pb(i);
v[i] = ll(ub - i) * h[i];
ll now = 0;
tmp.pb(ub);
rrep(j, SZ(tmp) - 1) {
chmin(v[i], v[tmp[j]] + now + (ll) h[tmp[j]] * (tmp[j] - i - 1) + h[i]);
now += (ll) h[tmp[j]] * (tmp[j + 1] - tmp[j]);
}
}
st.clear();
vl sum(n);
vi ord(q);
iota(all(ord), 0);
sort(all(ord), [&](int i, int j) { return l[i] > l[j]; });
int it = 0;
vl sub(q);
rrep(i, n) {
while (not st.empty() and h[st.back()] < h[i]) st.pop_back();
if (st.empty()) sum[i] = ll(n - i) * h[i];
else {
sum[i] = (ll) (st.back() - i) * h[i] + sum[st.back()];
v[i] += sum[st.back()];
}
st.pb(i);
while (it < q and l[ord[it]] == i) {
auto lb = lower_bound(all(st), r[ord[it]], [&](int val, int key) { return val >= key; });
if (lb != st.begin()) {
sub[ord[it]] = sum[*prev(lb)] + ll(*prev(lb) - r[ord[it]]) * h[*lb];
} else {
sub[ord[it]] = (ll) (n - r[ord[it]]) * h[*lb];
}
ans[ord[it]] = (ll) (r[ord[it]] - l[ord[it]]) * h[*lb];
++it;
}
}
// rep(i, n) cerr << h[i] << ' ' << v[i] << ' ' << lim[i] << ' ' << sum[i] << endl;
// rep(i, q) cerr << sub[i] << endl;
sort(all(ord), [&](int i, int j) { return r[i] < r[j]; });
it = 0;
LCT lct(n);
st.clear();
rep2(i, 1, n + 1) {
while (not st.empty() and h[st.back()] <= h[i - 1]) {
int now = st.back();
st.pop_back();
lct.add_segment(lim[now], now + 1, line(-h[now], (ll) h[now] * now + v[now]));
}
st.pb(i - 1);
while (it < q and r[ord[it]] == i) {
chmin(ans[ord[it]], lct.get_min(l[ord[it]]) - sub[ord[it]]);
++it;
}
}
for (int &i: l) i = n - i;
for (int &i: r) i = n - i;
rep(i, q) swap(l[i], r[i]);
reverse(all(h));
}
for(ll &i : ans) assert(i < linf);
return ans;
}
