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/* Pham Ngoc Tho aka Chis Pham                           */
/* [Author : Pham Ngoc Tho] - THPT Chuyen Nguyen Du      */
/* [ 2024 - 12TH GO VOI 24 ] - From Nguyen Du with love  */
// #pragma GCC optimize("O3,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include<bits/stdc++.h>
using namespace std;
#define oo 0x3f
#define ff first
#define ss second
#define endl "\n"
#define ins insert
#define chis id<<1
#define pham (id<<1) + 1
#define sqr(x) ((x) * 1ll * (x))
#define gcd(a, b) __gcd(a, b)
#define pb push_back
#define eb emplace_back
#define all(x) x.begin(), x.end()
#define allr(x) x.rbegin(),x.rend()
#define repu(i, x, n) for(int i = x; i <= n; ++i)
#define repd(i, n, x) for(int i = n; i >= x; --i)
#define reset(x, val) memset(x, val, sizeof(x))
typedef double db;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
template<class T> bool getbit(T val, int i) { return (val >> i) & 1; }
template<class T> int cntbit(T val)        { return val == 0 ? 0 : cntbit(val >> 1) + (val & 1); }
template<class T> ll fpow(T a, const T b) { ll res = 1, x = a, y = b; while(y){if(y & 1)res *= x; x = x * x; y>>=1;}; return res; }
template<class T> ll modfpow(T a, T b, const T &m) { ll res = 1, x = a, y = b; x %= m; while(y){if(y & 1){res *= x; res %= m;}; x = x * x; x %= m; y >>= 1; } return res % m; }
template<class T> T lcm(T &a, T &b) { return a / gcd(a, b) * b; }
const int mod = 1e9 + 7;
const int INF = 1e9 + 7;
const ll LNF = 1e18 + 7;
inline char gc() { static char buf[1 << 23]; static size_t bc, be; if(bc >= be){ buf[0] = 0, bc = 0; be = fread(buf, 1, sizeof(buf), stdin); } return buf[bc++]; }
ll readLL() { ll a, c; while ((a = gc()) < 20); if (a == '-') return -readLL(); while ((c = gc()) >= 48) a = a * 10 + c - 480; return a - 48; }
int readInt() { int a, c; while ((a = gc()) < 10); if (a == '-') return -readInt(); while ((c = gc()) >= 48) a = a * 10 + c - 480; return a - 48; }
mt19937 RND(time(nullptr));
ll rnd(ll l, ll r)
{
    assert(l <= r);ll L = l, R = r;
    ll aft = (L + RND() * 1LL % (R - L + 1));
    return aft;
}
#define TASK "name"
#define FILE "DEBUG"
void setIO()
{
    ios_base::sync_with_stdio(0);
    cin.tie(0);cout.tie(0);
    if(fopen(FILE".INP", "r")){freopen(FILE".INP", "r", stdin);freopen(FILE".OUT", "w", stdout);}
    if(fopen(TASK".INP", "r")){freopen(TASK".INP", "r", stdin);freopen(TASK".OUT", "w", stdout);}
}
template<class T> T multi(const T &a, const T &b) { T res = (a*b)%mod; return res;}
template<class T> bool umax(T &a, T b) { if(a < b){ a = b; return 1;} else return 0;}
template<class T> bool umin(T &a, T b) { if(a > b){ a = b; return 1;} else return 0;}
const int NmX = 5e5 + 7;
const int dx[] = {0, 0, 1, -1};
const int dy[] = {1, -1, 0, 0};
int n;
ll a[NmX];
void read()
{
    cin >> n;
    repu(i, 1, n) cin >> a[i];
}
namespace sub2{
    const int N = 5e3 + 7;
    class IT{
        public:
            int it[4 * N];
            void build(int id, int l, int r){
                if(l == r){
                    it[id] = a[l];
                    return;
                }
                int mid = (l + r) >> 1;
                build(chis, l, mid);
                build(pham, mid + 1, r);
                it[id] = max(it[chis], it[pham]);
            }
            int get(int id, int l, int r, int u, int v){
                if(r < u || v < l) return -INF;
                if(u <= l && r <= v) return it[id];
                int mid = (l + r) >> 1;
                return max(get(chis, l, mid, u, v), get(pham, mid + 1, r, u, v));
            }
    }IT;
    ll f[N][N], fi[N][N];
    void solve(){
        IT.build(1, 1, n);
        repu(i, 1, n)
        {
            repu(j, i + 2, n)
            {
                int k = (i + j)/2;
                f[i][j] = a[i] + a[j] + IT.get(1, 1, n, i + 1, k);
                umax(f[i][j], f[i][j - 1]);
            }
        }
        repd(i, n, 1){
            repu(j, 1, n)
                umax(f[i - 1][j], f[i][j]);
        }        
        int q; cin >> q;
        while(q--){
            int u, v;
            cin >> u >> v;
            cout << f[u][v] << endl;
        }
    }
}
namespace sub3{
    const int N = 2e5 + 7;
    ll pre[2 * N];
    void solve(){
        stack<int> st;
        repu(i, 1, n){
            while(st.size() && a[st.top()] < a[i]){
                umax(pre[2 * i - st.top()], a[i] + a[st.top()]);
                st.pop();
            }
            if(st.size()) umax(pre[2 * i - st.top()], a[i] + a[st.top()]);
            st.push(i);
        }
        repu(i, 1, n) umax(pre[i], pre[i - 1]);
        ll res = 0;
        repu(i, 1, n) umax(res, pre[i] + a[i]);
        cout << res; 
    }
}
namespace sub4{
    vector<pii> qr[NmX], upd[NmX];
    int res[NmX];
    struct node{
        int pre, val, sum;
        node(){ pre = val = sum = 0; };
        node(int pre, int val, int sum) : pre(pre), val(val), sum(sum) {};
        friend node operator + (const node &x, const node &y){
            return node(max(x.pre, y.pre), max(x.val, y.val), max({x.sum, y.sum, x.pre + y.val}));
        }
    };
    node it[4 * NmX];
    void build(int id, int l, int r){
        if(l == r){
            it[id] = node(0, a[l], a[l]);
            return;
        }
        int mid = (l + r) >> 1;
        build(chis, l, mid);
        build(pham, mid + 1, r);
        it[id] = it[chis] + it[pham];
    }
    void update(int id, int l, int r, int pos, int val){
        if(r < pos || pos < l) return;
        if(l == r && r == pos){
            umax(it[id].pre, val);
            it[id].sum = it[id].pre + it[id].val;
            return;
        }
        int mid = (l + r) >> 1;
        update(chis, l, mid, pos, val);
        update(pham, mid + 1, r, pos, val);
        it[id] = it[chis] + it[pham];
    }
    node query(int id, int l, int r, int u, int v){
        if(r < u || v < l) return node(0, 0, 0);
        if(u <= l && r <= v) return it[id];
        int mid = (l + r) >> 1;
        return query(chis, l, mid, u, v) + query(pham, mid + 1, r, u, v);
    }
    void solve(){
        int q; cin >> q;
        repu(i, 1, q){
            int l, r;
            cin >> l >> r;
            qr[l].eb(pii(r, i));
        }
        build(1, 1, n);
        stack<int> st;
        repu(i, 1, n){
            while(st.size() && a[st.top()] < a[i]){
                int j = st.top();
                upd[j].eb(pii(i, a[i] + a[j]));
                st.pop();
            }
            if(st.size())
                upd[st.top()].eb(pii(i, a[i] + a[st.top()]));
            st.push(i);
        }    
        repd(i, n, 1){  
            for(pii x : upd[i]) 
                if(2 * x.ff - i <= n) 
                    update(1, 1, n, 2 * x.ff - i, x.ss);
            for(pii x : qr[i])
                res[x.ss] = query(1, 1, n, i, x.ff).sum;
        }
        repu(i, 1, q) cout << res[i] << endl;
    }
}
void process()
{
    // if(n <= 5000) sub2::solve();
    // else sub3::solve();
    sub4::solve();
}
main()
{
    setIO();
    int test = 1;
    // cin >> test;
    while(test--)
    {
        read();
        process();
    }
    cerr << "Time elapsed: " << (1.0 * clock()/CLOCKS_PER_SEC) * 1000 << "ms.\n";
    return 0;
}
컴파일 시 표준 에러 (stderr) 메시지
jumps.cpp:250:1: warning: ISO C++ forbids declaration of 'main' with no type [-Wreturn-type]
  250 | main()
      | ^~~~
jumps.cpp: In function 'void setIO()':
jumps.cpp:62:39: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   62 |     if(fopen(FILE".INP", "r")){freopen(FILE".INP", "r", stdin);freopen(FILE".OUT", "w", stdout);}
      |                                ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
jumps.cpp:62:71: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   62 |     if(fopen(FILE".INP", "r")){freopen(FILE".INP", "r", stdin);freopen(FILE".OUT", "w", stdout);}
      |                                                                ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~
jumps.cpp:63:39: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   63 |     if(fopen(TASK".INP", "r")){freopen(TASK".INP", "r", stdin);freopen(TASK".OUT", "w", stdout);}
      |                                ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~
jumps.cpp:63:71: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)' declared with attribute 'warn_unused_result' [-Wunused-result]
   63 |     if(fopen(TASK".INP", "r")){freopen(TASK".INP", "r", stdin);freopen(TASK".OUT", "w", stdout);}
      |                                                                ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~~~~| # | Verdict  | Execution time | Memory | Grader output | 
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