#include "secret.h"
#include <bits/stdc++.h>
using namespace std;
int MX_lv = 20;
int n;
vector<int> arr;
vector<vector<vector<int>>> dat;
int inf = 1e9 + 11;
void divi(int l, int r, int level) {
if (l == r) return;
assert(level < MX_lv);
int mid = (l + r) / 2;
dat[mid][level][0] = arr[mid];
dat[mid + 1][level][1] = arr[mid + 1];
for (int i = mid - 1; i >= l; i--) {
dat[i][level][0] = Secret(arr[i], dat[i + 1][level][0]);
}
for (int i = mid + 2; i <= r; i++) {
dat[i][level][1] = Secret(arr[i], dat[i - 1][level][1]);
}
divi(l, mid, level + 1);
divi(mid + 1, r, level + 1);
}
void Init(int N, int A[]) {
n = N;
arr.resize(n);
dat = vector<vector<vector<int>>>(N, vector<vector<int>>(MX_lv, vector<int>(2)));
for (int i = 0; i < n; i++) {
arr[i] = A[i];
}
divi(0, n - 1, 0);
// for (int k = 0; k < 2; k++) {
// for (int i = 0; i < MX_lv; i++) {
// for (int j = 0; j < n; j++) {
// cout << dat[j][i][k] << ' ';
// }
// cout << endl;
// }
// cout << endl;
// }
}
int Query(int L, int R) { // do something
if (L == R) return arr[L];
// now somehow figure out the level -> binary search
int hi = n - 1, lo = 0;
int lv = 0;
while (hi >= lo) {
int mid = (hi + lo) / 2;
if (L <= mid && mid < R) {
return Secret(dat[L][lv][0], dat[R][lv][1]);
} else if (R == mid) {
return dat[L][lv][0];
} else if (R <= mid) {
hi = mid - 1;
} else {
lo = mid + 1;
}
lv++;
}
assert(0);
return 0;
}
