#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int N = 1e5 + 2, SQR = 900;
int nxtL[N], nxtR[N];
vector <int> height;
int cost(int l, int r, int u) {
int ans = 0;
for (int i = u; i >= l;) {
int k = max(l, nxtL[i] + 1);
ans += height[i] * (i - k + 1);
i = k - 1;
}
for (int i = u; i <= r;) {
int k = min(r, nxtR[i] - 1);
ans += height[i] * (k - i + 1);
i = k + 1;
}
return ans -= height[u];
}
int cache[SQR + 1][N];
int dnc(int l, int r) {
if (l > r) return 1e9;
if (l == r) return height[l];
if (r - l <= SQR && cache[r - l][l])
return cache[r - l][l];
int mid = (l + r) >> 1; int ans = 2e9;
int le[20], ri[20], lSize = 0, rSize = 0;
for (int i = mid; i >= l; i = nxtL[i]) le[lSize++] = i;
reverse(le, le + lSize);
for (int i = mid + 1; i <= r; i = nxtR[i]) ri[rSize++] = i;
int id = rSize - 1, sumL = 0, sumR = 0;
for (int i = 0; i < lSize; i++) {
int pos = le[i];
int k = max(nxtL[pos] + 1, l); // k -> pos
if (l < k) {
int B = nxtL[pos];
int A = max(nxtL[B] + 1, l);
sumL += (B - A + 1) * height[B];
}
int R = min(r + 1, nxtR[pos]);
while (id >= 0 && ri[id] >= R) {
if (id == rSize - 1) sumR += (r - ri[id] + 1) * height[ri[id]];
else sumR += (ri[id + 1] - ri[id]) * height[ri[id]];
--id;
}
int costL = sumL + dnc(k, pos) + height[pos] * (mid - pos);
int costR = height[pos] * (R - 1 - mid) + sumR;
ans = min(ans, costL + costR);
}
reverse(ri, ri + rSize);
id = sumL = sumR = 0;
for (int i = 0; i < rSize; i++) {
int pos = ri[i];
int k = min(nxtR[pos] - 1, r);
if (k < r) {
int A = nxtR[pos];
int B = min(nxtR[A] - 1, r);
sumR += (B - A + 1) * height[A];
}
int L = max(nxtL[pos], l - 1);
while (id < lSize && le[id] <= L) {
if (id == 0) sumL += (le[id] - l + 1) * height[le[id]];
else sumL += (le[id] - le[id - 1]) * height[le[id]];
++id;
}
int costL = sumL + height[pos] * (mid - L);
int costR = (pos - 1 - mid) * height[pos] + dnc(pos, k) + sumR;
ans = min(ans, costL + costR);
}
if (r - l <= SQR) cache[r - l][l] = ans;
return ans;
}
ll pref[5005][5005];
vector <ll> minimum_costs(vector <int> H, vector <int> L, vector <int> R) {
int n = H.size();
if (*max_element(H.begin(), H.end()) <= 20) {
height = H; stack <int> st;
for (int i = 0; i < n; i++) {
while (!st.empty() && H[st.top()] <= H[i]) st.pop();
nxtL[i] = (st.empty() ? -1 : st.top()); st.emplace(i);
}
while (!st.empty()) st.pop();
for (int i = n - 1; i >= 0; i--) {
while (!st.empty() && H[st.top()] <= H[i]) st.pop();
nxtR[i] = (st.empty() ? n : st.top()); st.emplace(i);
}
vector <ll> ans;
for (int i = 0; i < L.size(); i++)
ans.emplace_back(dnc(L[i], R[i]));
return ans;
}
else {
for (int i = 0; i < n; i++) {
pref[i][i] = height[i];
for (int j = i - 1, ma = height[i]; j >= 0; j--) {
ma = max(ma, height[j]);
pref[i][j] = ma;
}
for (int j = i + 1, ma = height[i]; j < n; j++) {
ma = max(ma, height[j]);
pref[i][j] = ma;
}
for (int j = 1; j < n; j++) pref[i][j] += pref[i][j - 1];
}
auto get = [&] (int u, int l, int r) {
if (l == 0) return pref[u][r];
return pref[u][r] - pref[u][l - 1];
};
vector <ll> ans;
for (int i = 0; i < L.size(); i++) {
ll res = 1e18;
for (int u = L[i]; u <= R[i]; u++)
res = min(res, get(u, L[i], R[i]));
ans.emplace_back(res);
}
return ans;
}
}
