#include <bits/stdc++.h>
//#pragma GCC optimize("unroll-loops")
//#pragma GCC optimize("-O3")
//#pragma GCC optimize("Ofast")
//#pragma GCC optimize("fast-math")
//#pragma GCC optimize("no-stack-protector")
#define F first
#define S second
#define sz(x) int(x.size())
#define pb push_back
#define pf push_front
#define N 5005
#define M ll(998244353)
#define inf 1e9 + 1e9
using namespace std;
typedef long double ld;
typedef long long ll;
typedef unsigned long long ull;
typedef short int si;
typedef array <ll, 3> a3;
typedef array <ll, 4> a4;
ll t[N * 4], trr[N * 4];
int mx[N * 4], psh[N * 4], pshr[N * 4];
vector <int> a;
void Push(int v, int tl, int tr)
{
if (psh[v] == 0) return;
t[v] = ll(psh[v]) * ll(tr - tl + 1);
if (tl != tr) psh[v + v] = psh[v + v + 1] = psh[v];
psh[v] = 0;
}
void Pushr(int v, int tl, int tr)
{
if (pshr[v] == 0) return;
trr[v] = ll(pshr[v]) * ll(tr - tl + 1);
if (tl != tr) pshr[v + v] = pshr[v + v + 1] = pshr[v];
pshr[v] = 0;
}
void upd(int v, int tl, int tr, int l, int r, int val)
{
Push(v, tl, tr);
if (r < tl || tr < l || l > r) return;
if (l <= tl && tr <= r) {psh[v] = val; Push(v, tl, tr); return;}
int md = (tl + tr) >> 1;
upd(v + v, tl, md, l, r, val); upd(v + v + 1, md + 1, tr, l, r, val);
t[v] = t[v + v] + t[v + v + 1];
}
void updr(int v, int tl, int tr, int l, int r, int val)
{
Pushr(v, tl, tr);
if (r < tl || tr < l || l > r) return;
if (l <= tl && tr <= r) {pshr[v] = val; Pushr(v, tl, tr); return;}
int md = (tl + tr) >> 1;
updr(v + v, tl, md, l, r, val); updr(v + v + 1, md + 1, tr, l, r, val);
trr[v] = trr[v + v] + trr[v + v + 1];
}
ll sm(int v, int tl, int tr, int l, int r)
{
Push(v, tl, tr);
if (r < tl || tr < l || l > r) return 0ll;
if (l <= tl && tr <= r) return t[v];
int md = (tl + tr) >> 1;
return sm(v + v, tl, md, l, r) + sm(v + v + 1, md + 1, tr, l, r);
}
ll smr(int v, int tl, int tr, int l, int r)
{
Pushr(v, tl, tr);
if (r < tl || tr < l || l > r) return 0ll;
if (l <= tl && tr <= r) return trr[v];
int md = (tl + tr) >> 1;
return smr(v + v, tl, md, l, r) + smr(v + v + 1, md + 1, tr, l, r);
}
int fndl(int v, int tl, int tr, int l, int r, int val)
{
if (mx[v] <= val || l > r || r < tl || tr < l) return -1;
if (tl == tr) return tl;
int md = (tl + tr) >> 1;
int vt = -1;
if (mx[v + v] > val) vt = fndl(v + v, tl, md, l, r, val);
if (vt == -1) vt = fndl(v + v + 1, md + 1, tr, l, r, val);
return vt;
}
int fndr(int v, int tl, int tr, int l, int r, int val)
{
if (mx[v] <= val || l > r || r < tl || tr < l) return -1;
if (tl == tr) return tl;
int md = (tl + tr) >> 1;
int vt = -1;
if (mx[v + v + 1] > val) vt = fndr(v + v + 1, md + 1, tr, l, r, val);
if (vt == -1) vt = fndr(v + v, tl, md, l, r, val);
return vt;
}
void bld(int v, int tl, int tr)
{
if (tl == tr) mx[v] = a[tl];
else
{
int md = (tl + tr) >> 1;
bld(v + v, tl, md);
bld(v + v + 1, md + 1, tr);
mx[v] = max(mx[v + v], mx[v + v + 1]);
}
}
vector <ll> minimum_costs (vector <int> h, vector <int> l, vector <int> r)
{
int q = sz(l);
int n = sz(h);
vector <ll> ans(q);
ll val[n], pr[n][n], sf[n][n];
a = h;
bld(1, 0, n - 1);
int mxn = 0;
upd(1, 0, n - 1, 0, n - 1, 0);
for (register int j = 0; j <= n - 1; j++)
{
if (mxn == 0 || mxn <= h[j]) upd(1, 0, n - 1, 0, j, h[j]);
else
{
int it = fndr(1, 0, n - 1, 0, j - 1, h[j]);
upd(1, 0, n - 1, it + 1, j, h[j]);
}
pr[j][j] = sm(1, 0, n - 1, 0, j);
for (int u = j - 1; u >= 0; u--) pr[j][u] = sm(1, 0, n - 1, 0, u);
val[j] = pr[j][j];
mxn = max(mxn, h[j]);
}
updr(1, 0, n - 1, 0, n - 1, 0);
mxn = 0;
for (register int j = n - 1; j >= 0; j--)
{
if (mxn == 0 || mxn <= h[j]) updr(1, 0, n - 1, j, n - 1, h[j]);
else
{
int it = fndl(1, 0, n - 1, j + 1, n - 1, h[j]);
updr(1, 0, n - 1, j, it - 1, h[j]);
}
sf[j][j] = smr(1, 0, n - 1, j, n - 1);
for (int u = j + 1; u <= n - 1; u++) sf[j][u] = sm(1, 0, n - 1, u, n - 1);
val[j] += smr(1, 0, n - 1, j + 1, n - 1);
mxn = max(mxn, h[j]);
}
for (int i = 0; i < q; i++)
{
ll mn = 1e18;
for (int j = l[i]; j <= r[i]; j++)
mn = min(mn, val[j] - (l[i] == 0 ? 0 : pr[j][l[i] - 1]) - (r[i] == n - 1 ? 0 : sf[j][r[i] + 1]));
ans[i] = mn;
}
return ans;
}
