#include <bits/stdc++.h>
#include "secret.h"
using namespace std;
const int maxn = 1001;
int pref [maxn][maxn];
int sg [maxn][maxn];
void build (int l, int r) {
if (l >= r) return;
int mid = (l + r) / 2;
for (int i = l; i <= mid; i++){
for (int j = mid + 1; j <= r; j++){
sg[i][j] = mid;
}
}
for (int i = mid + 2; i <= r; i++){
pref[mid + 1][i] = Secret(pref[mid + 1][i-1], pref[i][i]);
}
for (int i = mid - 1; i >= l; i--){
pref[i][mid] = Secret(pref[i][i], pref[i + 1][mid]);
}
build (l, mid);
build (mid + 1, r);
}
void Init(int N, int A[]) {
for (int i = 0; i < N; i++){
for (int j = 0; j < N; j++) {
pref[i][j] = -1;
}
}
for (int i = 0; i < N; i++){
pref[i][i] = A[i];
}
build(0, N);
}
int Query(int L, int R) {
if (pref[L][R] != -1) return pref[L][R];
int mid = sg[L][R];
return Secret(pref[L][mid], pref[mid + 1][R]);
}
