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#include "meetings.h"
#include <bits/stdc++.h>
using namespace std;
template<class C>constexpr int sz(const C&c){return int(c.size());}
using ll=long long;constexpr const char nl='\n',sp=' ';
template <class T, class F> struct SparseTable {
int N, lg; vector<vector<T>> ST; F op;
void build() { for (int i = 0; i < lg - 1; i++) for (int j = 0; j < N; j++) ST[i + 1][j] = op(ST[i][j], ST[i][min(j + (1 << i), N - 1)]); }
template <class It> SparseTable(It st, It en, F op) : N(en - st), lg(32 - __builtin_clz(N)), ST(lg, vector<T>(st, en)), op(op) { build(); }
template <class It> SparseTable(It st, It en) : SparseTable(st, en, F()) {}
// 0-indexed, inclusive
T query(int l, int r) { int i = 31 - __builtin_clz(r - l + 1); return op(ST[i][l], ST[i][r - (1 << i) + 1]); }
};
template <class It, class F> auto makeSparseTable(It st, It en, F op) {
return SparseTable<typename std::iterator_traits<It>::value_type, F>(st, en, op);
}
using T = ll; const T NEG_INF = (numeric_limits<T>::lowest)() / 2;
T add(T a, T b) {
if (a == NEG_INF || b == NEG_INF) return NEG_INF;
return max(NEG_INF, a + b);
}
struct Line {
T m, b;
Line(T m = 0, T b = NEG_INF) : m(m), b(b) {}
T eval(int x) const { return add(m * x, b); }
void addConstant(T C) { b = add(b, C); }
bool majorize(const Line &line, int l, int r) const { return eval(l) >= line.eval(l) && eval(r) >= line.eval(r); }
};
template <const int MAXN, const bool ONE_INDEXED, const bool maxHull> struct LiChaoTree {
int N; Line TR[MAXN * 2]; T LZ[MAXN * 2];
void init(int size) { N = size; fill(TR, TR + N * 2, Line()); fill(LZ, LZ + N * 2, 0); }
void propagate(int cur, int tl, int tr) {
if (LZ[cur] != 0) {
int m = tl + (tr - tl) / 2, rc = cur + (m - tl + 1) * 2;
TR[cur + 1].addConstant(LZ[cur]);
LZ[cur + 1] = add(LZ[cur + 1], LZ[cur]);
TR[rc].addConstant(LZ[cur]);
LZ[rc] = add(LZ[rc], LZ[cur]);
LZ[cur] = 0;
}
}
void addConstant(int cur, int tl, int tr, int l, int r, T C) {
if (r < tl || tr < l) return;
if (l <= tl && tr <= r) { TR[cur].addConstant(C); LZ[cur] = add(LZ[cur], C); return; }
int m = tl + (tr - tl) / 2, rc = cur + (m - tl + 1) * 2; propagate(cur, tl, tr);
addConstant(cur + 1, tl, m, l, r, C); addConstant(rc, m + 1, tr, l, r, C);
}
void addLine(int cur, int tl, int tr, Line line) {
if (tl != tr) propagate(cur, tl, tr);
if (line.majorize(TR[cur], tl, tr)) swap(line, TR[cur]);
if (TR[cur].majorize(line, tl, tr)) return;
if (TR[cur].eval(tl) < line.eval(tl)) swap(line, TR[cur]);
int m = tl + (tr - tl) / 2, rc = cur + (m - tl + 1) * 2;
if (line.eval(m) >= TR[cur].eval(m)) { swap(line, TR[cur]); addLine(cur + 1, tl, m, line); }
else addLine(rc, m + 1, tr, line);
}
void addLineSegment(int cur, int tl, int tr, int l, int r, Line line) {
if (r < tl || tr < l) return;
if (l <= tl && tr <= r) { addLine(cur, tl, tr, line); return; }
int m = tl + (tr - tl) / 2, rc = cur + (m - tl + 1) * 2; propagate(cur, tl, tr);
addLineSegment(cur + 1, tl, m, l, r, line); addLineSegment(rc, m + 1, tr, l, r, line);
}
T getMax(int cur, int tl, int tr, int x) {
T ret = TR[cur].eval(x);
if (tl == tr) return ret;
int m = tl + (tr - tl) / 2, rc = cur + (m - tl + 1) * 2; propagate(cur, tl, tr);
if (x <= m) return max(ret, getMax(cur + 1, tl, m, x));
else return max(ret, getMax(rc, m + 1, tr, x));
}
void addConstant(int l, int r, T C) { addConstant(0, ONE_INDEXED, N - !ONE_INDEXED, l, r, maxHull ? C : -C); }
void addLine(Line line) { addLine(0, ONE_INDEXED, N - !ONE_INDEXED, maxHull ? line : Line(-line.m, -line.b)); }
void addLineSegment(Line line, int l, int r) {
addLineSegment(0, ONE_INDEXED, N - !ONE_INDEXED, l, r, maxHull ? line : Line(-line.m, -line.b));
}
T getMax(int x) { T ret = getMax(0, ONE_INDEXED, N - !ONE_INDEXED, x); return maxHull ? ret : -ret; }
};
const int MAXN = 750005;
LiChaoTree<MAXN, 0, false> lLines, rLines;
vector<ll> minimum_costs(vector<int> H, vector<int> L, vector<int> R) {
int N = sz(H), Q = sz(L);
vector<int> P(N, 0);
iota(P.begin(), P.end(), 0);
auto ST = makeSparseTable(P.begin(), P.end(), [&] (const int &i, const int &j) { return H[i] > H[j] ? i : j; });
vector<ll> ans(Q, LLONG_MAX);
vector<vector<int>> queries(N);
for (int i = 0; i < Q; i++) {
if (L[i] == R[i]) ans[i] = H[L[i]];
else queries[ST.query(L[i], R[i])].push_back(i);
}
lLines.init(N);
rLines.init(N);
function<void(int, int)> solve = [&] (int l, int r) {
if (l > r) return;
int m = ST.query(l, r);
ll hm = H[m];
solve(l, m - 1);
solve(m + 1, r);
for (int i : queries[m]) ans[i] = min(lLines.getMax(L[i]) + (R[i] - m + 1) * hm, rLines.getMax(R[i]) + (m - L[i] + 1) * hm);
if (l < m) lLines.addConstant(l, m - 1, (r - m + 1) * hm);
if (m < r) rLines.addConstant(m + 1, r, (m - l + 1) * hm);
lLines.addLineSegment(Line(-hm, (m < r ? lLines.getMax(m + 1) : 0) + (m + 1) * hm), l, m);
rLines.addLineSegment(Line(hm, (l < m ? rLines.getMax(m - 1) : 0) - (m - 1) * hm), m, r);
};
solve(0, N - 1);
return ans;
}
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