#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int MX = 750002;
inline ll divFloor(ll a, ll b){
if(a>=0) return a/b;
else return -((-a+b-1)/b);
}
inline ll divCeil(ll a, ll b){
if(b<0) a=-a, b=-b;
return divFloor(a+b-1, b);
}
int n, q;
ll arr[MX];
int ql[MX], qr[MX];
ll ans[MX];
void solve();
vector<ll> minimum_costs(vector<int> H, vector<int> L, vector<int> R){
n = (int)H.size();
for(int i=1; i<=n; i++) arr[i] = H[i-1];
q = (int)L.size();
for(int i=1; i<=q; i++) ql[i] = L[i-1]+1, qr[i] = R[i-1]+1, ans[i] = LLONG_MAX;
solve();
vector<ll> ret;
for(int i=1; i<=q; i++) ret.push_back(ans[i]);
return ret;
}
void makeCartesianTree();
void reformQuery();
void calculateAnswer();
int mult = 1;
void solve(){
makeCartesianTree();
reformQuery();
calculateAnswer();
reverse(arr+1, arr+n+1);
for(int i=1; i<=q; i++) ql[i] = n+1-ql[i], qr[i] = n+1-qr[i], swap(ql[i], qr[i]);
mult = -1;
makeCartesianTree();
reformQuery();
calculateAnswer();
}
struct segTree{
pair<int, int> tree[1<<21];
void init(int i, int l, int r, ll *A){
if(l==r){
tree[i] = make_pair(A[l], l * mult);
return;
}
int m = (l+r)>>1;
init(i*2, l, m, A);
init(i*2+1, m+1, r, A);
tree[i] = max(tree[i*2], tree[i*2+1]);
}
pair<int, int> query(int i, int l, int r, int s, int e){
if(r<s || e<l) return make_pair(0, 0);
if(s<=l && r<=e) return tree[i];
int m = (l+r)>>1;
return max(query(i*2, l, m, s, e), query(i*2+1, m+1, r, s, e));
}
} tree;
int par[MX], lc[MX], rc[MX];
int intvL[MX], intvR[MX], root;
int thisL[MX];
int dnc(int l, int r, int p=0){
if(l>r) return 0;
int x = mult * tree.query(1, 1, n, l, r).second;
par[x] = p;
intvL[x] = l, intvR[x] = r;
lc[x] = dnc(l, x-1);
rc[x] = dnc(x+1, r);
thisL[intvL[x]] = x;
// printf("thisL[%d] = %d\n", intvL[x], x);
return x;
}
void makeCartesianTree(){
for(int i=1; i<=n; i++){
par[i] = lc[i] = rc[i] = thisL[i] = 0;
}
tree.init(1, 1, n, arr);
root = dnc(1, n);
}
vector<int> vec[MX];
void reformQuery(){
for(int i=1; i<=n; i++) vec[i].clear();
for(int i=1; i<=q; i++){
if(ql[i] == qr[i]){
ans[i] = arr[ql[i]];
continue;
}
int l = ql[i], r = qr[i], x = mult * tree.query(1, 1, n, l, r).second;
if(x==qr[i]) ans[i] = min(ans[i], arr[x] * (r-l+1));
else vec[thisL[x+1]].push_back(i);
//printf("Pushed %d to %d (x %d)\n", i, thisL[x+1], x);
}
}
ll lazy[MX]; int rEnd[MX];
ll setA[MX], setB[MX];
set<int> st;
int sz[MX];
ll backVal(int x, int loc){
int t = *prev(st.upper_bound(loc));
//printf("backVal[%d] = %lld (t=%d)\n", x, setA[t] * rEnd[t] + setB[t] + lazy[x], t);
return setA[t] * rEnd[t] + setB[t] + lazy[x];
}
ll calc(int x, ll v){
int p = *prev(upper_bound(st.begin(), st.end(), v));
return setA[p] * v + setB[p] + lazy[x];
}
void render(int x, ll a, ll b){
auto it = st.lower_bound(intvL[x]);
if(it==st.end() || *it > intvR[x] ||
setA[*it] * (*it) + setB[*it] + lazy[x] <= a*(*it)+b)
return;
ll L = *it, R = L-1;
while(it != st.end() && *it <= intvR[x]){
int f = *it;
if(setA[f] * f + setB[f] + lazy[x] <= a * f + b) break;
if(setA[f] * rEnd[f] + setB[f] + lazy[x] >= a * rEnd[f] + b){
R = rEnd[f];
++it, st.erase(prev(it)), sz[x]--;
continue;
}
ll ad = a - setA[f], bd = setB[f] + lazy[x] - b;
assert(ad > 0 && bd >= 0);
ll newL = divCeil(bd, ad);
R = newL - 1;
st.erase(it), st.insert(newL);
setA[newL] = setA[f], setB[newL] = setB[f], rEnd[newL] = rEnd[f];
if(newL != f) setA[f] = setB[f] = rEnd[f] = 0;
break;
}
//printf("After render, [%d - %d] is formed\n", L, R);
if(L<=R){
st.insert(L); sz[x]++;
rEnd[L] = R;
setA[L] = a, setB[L] = b - lazy[x];
//printf("set: ", x); for(int p: st) printf("%d ", p); puts("");
}
}
void merge(ll a, ll b){
if(sz[a] > sz[b]){
auto it = st.lower_bound(intvL[b]);
while(it != st.end() && *it <= intvR[b]) setB[*it] += lazy[b] - lazy[a], ++it;
}
else{
auto it = st.lower_bound(intvL[a]);
while(it != st.end() && *it <= intvR[a]) setA[*it] += lazy[a] - lazy[b], ++it;
lazy[a] = lazy[b];
}
sz[a] += sz[b];
}
void dnc(int x){
int L = intvL[x], R = intvR[x];
// printf("dnc %d %d %d\n", x, L, R);
/// [L, x]
if(lc[x]){
dnc(lc[x]);
lazy[x] = lazy[lc[x]];
setA[x] = 0, setB[x] = backVal(x, x-1) + arr[x] - lazy[x];
sz[x] = sz[lc[x]] + 1, sz[lc[x]] = 0;
}
else{
rEnd[x] = x;
setA[x] = 0, setB[x] = arr[x] - lazy[x];
}
if(rc[x]){
dnc(rc[x]);
/// DP[rc[x]] 앞부분을 다듬는다
ll v = backVal(x, x), vAll = arr[x] * (x-L+1);
// printf("Added %lld to %d\n", vAll, rc[x]);
lazy[rc[x]] += vAll;
render(rc[x], arr[x], v-arr[x]*x);
merge(x, rc[x]);
}
for(int idx: vec[x]){
ans[idx] = min(ans[idx], calc(x, qr[idx]) + arr[intvL[x]-1] * (intvL[x] - ql[idx]));
//printf("Checking %d: maybe %lld + %lld = %lld\n", idx, calc(x, qr[idx]), arr[intvL[x]-1]*(intvL[x]-ql[idx]),
// calc(x, qr[idx]) + arr[intvL[x]-1] * (intvL[x] - ql[idx]));
}
//printf("Deque of %d\n", x);
//for(int p: st) if(intvL[x] <= p && p <= intvR[x]) printf("[%d-%d] %lldx + %lld, \t", p, rEnd[p], setA[p], setB[p]+lazy[x]); puts("");
}
void calculateAnswer(){
st.clear();
for(int i=1; i<=n; i++){
lazy[i] = 0, rEnd[i] = i, setA[i] = setB[i] = 0, sz[i] = 1;
st.insert(i);
}
dnc(root);
}
