#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> pi;
typedef pair<ll, ll> pl;
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
#define pb push_back
#define f first
#define s second
namespace debug {
const int DEBUG = true;
template<class T1, class T2>
void pr(const pair<T1, T2> &x);
template<class T, size_t SZ>
void pr(const array<T, SZ> &x);
template<class T>
void pr(const vector<T> &x);
template<class T>
void pr(const set<T> &x);
template<class T1, class T2>
void pr(const map<T1, T2> &x);
template<class T>
void pr(const T &x) { if (DEBUG) cout << x; }
template<class T, class... Ts>
void pr(const T &first, const Ts &... rest) { pr(first), pr(rest...); }
template<class T1, class T2>
void pr(const pair<T1, T2> &x) { pr("{", x.f, ", ", x.s, "}"); }
template<class T>
void prIn(const T &x) {
pr("{");
bool fst = 1;
for (auto &a : x) {
pr(fst ? "" : ", ", a), fst = 0;
}
pr("}");
}
template<class T, size_t SZ>
void pr(const array<T, SZ> &x) { prIn(x); }
template<class T>
void pr(const vector<T> &x) { prIn(x); }
template<class T>
void pr(const set<T> &x) { prIn(x); }
template<class T1, class T2>
void pr(const map<T1, T2> &x) { prIn(x); }
void ps() { pr("\n"), cout << flush; }
template<class Arg, class... Args>
void ps(const Arg &first, const Args &... rest) {
pr(first, " ");
ps(rest...);
}
}
using namespace debug;
const int MAXN = 5e5 + 10;
int N, Q;
int val[MAXN];
int qL[MAXN], qR[MAXN];
int ans[MAXN];
struct LSegTr {
int tr[4 * MAXN + 5], lz[4 * MAXN + 5];
void push(int i, int l, int r) {
tr[i] += lz[i];
if (l != r) {
lz[i * 2] += lz[i];
lz[i * 2 + 1] += lz[i];
}
lz[i] = 0;
}
int q(int i, int l, int r, int s, int e) {
if (e < l || r < s) {
return 0;
}
push(i, l, r);
if (s <= l && r <= e) {
return tr[i];
}
int mid = (l + r) / 2;
return max(q(i * 2, l, mid, s, e), q(i * 2 + 1, mid + 1, r, s, e));
}
void u(int i, int l, int r, int s, int e, int d) {
push(i, l, r); // pushed early to use in recalculation of parent
if (e < l || r < s) {
return;
}
if (s <= l && r <= e) {
lz[i] += d;
push(i, l, r);
return;
}
int mid = (l + r) / 2;
u(i * 2, l, mid, s, e, d);
u(i * 2 + 1, mid + 1, r, s, e, d);
tr[i] = max(tr[i * 2], tr[i * 2 + 1]);
}
void b(int i, int l, int r) {
if (l == r) {
if (l >= N) {
return;
}
tr[i] = val[l];
return;
}
int mid = (l + r) / 2;
b(i * 2, l, mid);
b(i * 2 + 1, mid + 1, r);
tr[i] = max(tr[i * 2], tr[i * 2 + 1]);
}
} lSegTr;
set<pi> ints;
bool evaluate(pi nInt, pi oInt) {
if (nInt.s <= oInt.s) {
return false;
}
int delta = nInt.s - oInt.s;
int oIntR = ints.upper_bound(oInt)->f - 1;
int updL = max(nInt.f, oInt.f);
// ps("oInt:", oInt);
// ps("segTr adding");
// ps(updL, oIntR, delta);
lSegTr.u(1, 0, MAXN, updL, oIntR, delta);
if (nInt.f <= oInt.f) {
ints.erase(oInt);
}
return true;
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
cin >> N;
for (int i = 0; i < N; i++) {
cin >> val[i];
}
cin >> Q;
vector<pair<pi, int>> queries;
for (int i = 0; i < Q; i++) {
cin >> qL[i] >> qR[i];
qL[i]--, qR[i]--;
queries.pb({{qL[i], qR[i]}, i});
}
sort(queries.begin(), queries.end());
reverse(queries.begin(), queries.end());
vi stack;
vector<pi> lmInts;
for (int i = 0; i < N; i++) {
for (int j = stack.size() - 1; j >= 0; j--) {
lmInts.pb({stack[j], i});
if (val[stack[j]] >= val[i]) {
break;
}
}
while (stack.size() && val[stack[stack.size() - 1]] <= val[i]) {
stack.erase(--stack.end());
}
stack.pb(i);
}
// lmInts should contain all pairs of (l, m) s.t. all values with indices in-between are strictly less
sort(lmInts.begin(), lmInts.end());
reverse(lmInts.begin(), lmInts.end());
// ps(lmInts);
// ps(queries);
ints.insert({N, (int) 1e9});
ints.insert({N + 1, (int) 1e9});
ints.insert({0, 0});
memset(lSegTr.tr, 0, sizeof(lSegTr.tr));
memset(lSegTr.lz, 0, sizeof(lSegTr.lz));
lSegTr.b(1, 0, MAXN);
// ps(ints);
int nLM = 0, nQ = 0;
for (int i = N - 1; i >= 0; i--) {
while (nLM < lmInts.size() && i <= lmInts[nLM].f) {
pi cLM = lmInts[nLM];
int cLMVal = val[cLM.f] + val[cLM.s];
int r = cLM.s + cLM.s - cLM.f;
// ps("adding");
// ps(cLM.f, cLM.s, r, cLMVal);
pi nInt = {r, cLMVal};
pi cInt = *(--ints.upper_bound({r, (int) 1e9}));
bool lRes = true;
int sCnt = 0;
while (lRes) {
lRes = evaluate(nInt, cInt);
cInt = *ints.upper_bound(cInt);
sCnt++;
}
if (sCnt > 1) {
ints.insert(nInt);
}
nLM++;
// ps("post add");
// ps(ints);
}
while (nQ < Q && queries[nQ].f.f == i) {
int l = queries[nQ].f.f;
int r = queries[nQ].f.s;
int qI = queries[nQ].s;
// ps("querying", l, r, qI);
// if (true) {
// ps("spec", lSegTr.q(1, 0, MAXN, 3, 3));
// }
ans[qI] = lSegTr.q(1, 0, MAXN, l, r);
// ps(ans[qI]);
nQ++;
}
}
for (int i = 0; i < Q; i++) {
cout << ans[i] << '\n';
}
cout << flush;
}
