#include "meetings.h"
#include <bits/stdc++.h>
#include <bits/extc++.h>
#define StarBurstStream ios_base::sync_with_stdio(false); cin.tie(0); cout.tie(0);
#define iter(a) a.begin(), a.end()
#define riter(a) a.rbegin(), a.rend()
#define lsort(a) sort(iter(a))
#define gsort(a) sort(riter(a))
#define pb(a) push_back(a)
#define eb(a) emplace_back(a)
#define pf(a) push_front(a)
#define ef(a) emplace_front(a)
#define pob pop_back()
#define pof pop_front()
#define mp(a, b) make_pair(a, b)
#define F first
#define S second
#define mt make_tuple
#define gt(t, i) get<i>(t)
#define tomax(a, b) ((a) = max((a), (b)))
#define tomin(a, b) ((a) = min((a), (b)))
#define topos(a) ((a) = (((a) % MOD + MOD) % MOD))
#define uni(a) a.resize(unique(iter(a)) - a.begin())
#define printv(a, b) {bool pvaspace=false; \
for(auto pva : a){ \
if(pvaspace) b << " "; pvaspace=true;\
b << pva;\
}\
b << "\n";}
using namespace std;
using namespace __gnu_pbds;
typedef long long ll;
typedef unsigned long long ull;
typedef long double ld;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
using pdd = pair<ld, ld>;
using tiii = tuple<int, int, int>;
const ll MOD = 1000000007;
const ll MAX = 1LL << 60;
template<typename A, typename B>
ostream& operator<<(ostream& o, pair<A, B> p){
return o << '(' << p.F << ',' << p.S << ')';
}
ll ifloor(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a < 0) return (a - b + 1) / b;
else return a / b;
}
ll iceil(ll a, ll b){
if(b < 0) a *= -1, b *= -1;
if(a > 0) return (a + b - 1) / b;
else return a / b;
}
int n, q;
vector<ll> h;
struct SparseTable{
vector<vector<int>> st;
int argmin(int x, int y){
if(h[x] == h[y]) return x < y ? x : y;
else return h[x] > h[y] ? x : y;
}
void init(){
st.resize(20, vector<int>(n + 1));
iota(iter(st[0]), 0);
for(int i = 1; i < 20; i++){
for(int j = 1; j + (1 << i) - 1 <= n; j++){
st[i][j] = argmin(st[i - 1][j], st[i - 1][j + (1 << (i - 1))]);
}
}
}
int query(int l, int r){
int lg = __lg(r - l + 1);
return argmin(st[lg][l], st[lg][r - (1 << lg) + 1]);
}
};
SparseTable stb;
struct Node{
ll mn = 0, mx = 0;
ll a = 0, b = 0;
};
#define lc 2 * id + 1
#define rc 2 * id + 2
struct SegmentTree{
vector<Node> st;
void init(){
st.resize(4 * n);
}
void addtag(ll a, ll b, int L, int R, int id){
if(a == 0){
st[id].mn += b;
st[id].mx += b;
st[id].b += b;
}
else{
st[id].mn = a * L + b;
st[id].mx = a * R + b;
st[id].a = a;
st[id].b = b;
}
}
void push(int L, int R, int id){
int M = (L + R) / 2;
addtag(st[id].a, st[id].b, L, M, lc);
addtag(st[id].a, st[id].b, M + 1, R, rc);
st[id].a = st[id].b = 0;
}
void pull(int id){
st[id].mn = min(st[lc].mn, st[rc].mn);
st[id].mx = max(st[lc].mx, st[rc].mx);
}
void modify(int l, int r, ll a, ll b, int L = 1, int R = n, int id = 0){
if(l > r) return;
if(l <= L && R <= r){
if(a == 0){
addtag(a, b, L, R, id);
return;
}
if(st[id].mn <= min(L * a + b, R * a + b)) return;
if(st[id].mx >= max(L * a + b, R * a + b)){
addtag(a, b, L, R, id);
return;
}
}
push(L, R, id);
int M = (L + R) / 2;
if(r <= M) modify(l, r, a, b, L, M, lc);
else if(l > M) modify(l, r, a, b, M + 1, R, rc);
else{
modify(l, r, a, b, L, M, lc);
modify(l, r, a, b, M + 1, R, rc);
}
pull(id);
}
ll query(int x, int L = 1, int R = n, int id = 0){
if(L == R) return st[id].mn;
push(L, R, id);
int M = (L + R) / 2;
if(x <= M) return query(x, L, M, lc);
else return query(x, M + 1, R, rc);
}
};
SegmentTree stl, str;
vector<ll> ans;
vector<vector<int>> qry;
vector<int> L, R;
void dfs(int l, int r){
if(l > r) return;
int mid = stb.query(l, r);
dfs(l, mid - 1);
dfs(mid + 1, r);
for(int i : qry[mid]){
ans[i] = min(stl.query(L[i]) + (R[i] - mid + 1) * h[mid],
str.query(R[i]) + (mid - L[i] + 1) * h[mid]);
}
stl.modify(l, mid, 0, (r - mid + 1) * h[mid]);
str.modify(mid, r, 0, (mid - l + 1) * h[mid]);
if(l < mid){
ll tmp = str.query(mid - 1);
str.modify(mid, r, h[mid], h[mid] * (-mid + 1) + tmp);
}
if(mid < r){
ll tmp = stl.query(mid + 1);
stl.modify(l, mid, -h[mid], h[mid] * (mid + 1) + tmp);
}
/*cerr << "dfs " << l << " " << r << " " << mid << "\n";
for(int i = l; i < mid; i++) cerr << stl.query(i) << " ";
cerr << ", ";
cerr << stl.query(mid) << " " << str.query(mid) << " , ";
for(int i = mid + 1; i <= r; i++) cerr << str.query(i) << " ";
cerr << "\n";*/
}
vector<ll> minimum_costs(vector<int> H, vector<int> _L, vector<int> _R){
n = H.size();
q = _L.size();
h.resize(n + 1);
for(int i = 0; i < n; i++) h[i + 1] = H[i];
L = _L; R = _R;
for(int i = 0; i < q; i++) L[i]++, R[i]++;
ans.resize(q, MAX);
stb.init();
stl.init();
str.init();
qry.resize(n + 1);
for(int i = 0; i < q; i++){
int mid = stb.query(L[i], R[i]);
qry[mid].eb(i);
}
dfs(1, n);
return ans;
}
