#include "secret.h"
/*
* Author: Nonoze
* Created: Monday 22/12/2025
*/
#include <bits/stdc++.h>
using namespace std;
#ifndef DEBUG
#define dbg(...)
#endif
// #define cout cerr << "OUT: "
#define endl '\n'
#define endlfl '\n' << flush
#define quit(x) return (void)(cout << x << endl)
template<typename T> void read(T& x) { cin >> x; }
template<typename T1, typename T2> void read(pair<T1, T2>& p) { read(p.first), read(p.second); }
template<typename T> void read(vector<T>& v) { for (auto& x : v) read(x); }
template<typename T1, typename T2> void read(T1& x, T2& y) { read(x), read(y); }
template<typename T1, typename T2, typename T3> void read(T1& x, T2& y, T3& z) { read(x), read(y), read(z); }
template<typename T1, typename T2, typename T3, typename T4> void read(T1& x, T2& y, T3& z, T4& zz) { read(x), read(y), read(z), read(zz); }
template<typename T> void print(vector<T>& v) { for (auto& x : v) cout << x << ' '; cout << endl; }
#define sz(x) (int)(x.size())
#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define make_unique(v) sort(all(v)), v.erase(unique(all(v)), (v).end())
#define pb push_back
#define mp(a, b) make_pair(a, b)
#define fi first
#define se second
#define cmin(a, b) a = min(a, b)
#define cmax(a, b) a = max(a, b)
#define YES cout << "YES" << endl
#define NO cout << "NO" << endl
#define QYES quit("YES")
#define QNO quit("NO")
#define double long double
const int inf = numeric_limits<int>::max() / 4;
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
const int MOD = 1e9+7, LOG=20;
int val[1001][1001];
void calc(int l, int r, int A[]) {
if (l>=r) return;
int m=(l+r)/2;
calc(l, m-1, A);
calc(m+2, r, A);
for (int sz=1; m-sz>=l || m+1+sz<=r; sz++) {
if (m-sz>=l) {
int x=m-sz, y=m;
val[x][y]=Secret(A[x], val[x+1][y]);
}
if (m+sz+1<=r) {
int x=m+1, y=m+sz+1;
val[x][y]=Secret(val[x][y-1], A[y]);
}
}
}
void Init(int N, int A[]) {
for (int i=0; i<N; i++) {
for (int j=0; j<N; j++) val[i][j]=-1;
val[i][i]=A[i];
}
calc(0, N-1, A);
}
int Query(int L, int R) {
if (val[L][R]!=-1) return val[L][R];
for (int mid=L+1; mid<=R; mid++) {
if (val[L][mid-1]!=-1 && val[mid][R]!=-1) {
val[L][R]=Secret(val[L][mid-1], val[mid][R]);
return val[L][R];
}
}
assert(0);
return 0;
}
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