#include <bits/stdc++.h>
using namespace std;
using ll = long long;
//sub4:
vector<int> construct_range(int M, int K) {
vector<int> ans1 = {
4, 3, 1, 2, 1,
4, 3, 2, 7, 6,
5, 8, 11, 10, 9,
1, 7, 2, 3, 4,
};
if(M <= 20){
while(ans1.size() > M || ans1.back() >= M) ans1.pop_back();
return ans1;
}
vector<int> S = {0};
vector<bool> in_span(2*M, false);
int span_cnt = 0;
vector<pair<int,int>> pts;
while(span_cnt < M-1) {
int best_t = -1, best_gain = -1;
vector<bool> inS(2*M, false);
for(int u:S) inS[u] = true;
for(int t = 0; t <= 2*(M-1); t += 2) if(!inS[t]) {
int gain = 0;
for(int u:S) {
if(u==t) continue;
int s = u + t;
if(s >= 2 && s <= 2*(M-1) && (s%2==0) && !in_span[s]) ++gain;
}
if(gain > best_gain) {
best_gain = gain;
best_t = t;
}
}
if(best_t < 0) break;
for(int u:S) {
if(u == best_t) continue;
int s = u + best_t;
if(s >= 2 && s <= 2*(M-1) && (s%2==0) && !in_span[s]) {
int x = min(u, best_t), y = max(u, best_t);
pts.emplace_back(x, y);
in_span[s] = true;
++span_cnt;
}
}
S.push_back(best_t);
}
vector<int> H(M, 1);
for(auto [x,y] : pts) {
int idx = (x + y) / 2;
int h = (y - x) / 2;
if(idx >= 0 && idx < M) {
H[idx] = h;
}
}
return H;
}
/*long long count_triples(vector<int> H)
{
int n = H.size();
ll ans = 0;
for (int k = 0; k < n; k++)
{
int c = H[k];
int i = k - c;
if (i < 0 || i >= n) continue;
int a = H[i];
if (a > c - a) continue;
int need = c - a;
int j1 = i + a;
int j2 = k - a;
if (i < j1 && j1 < k && H[j1] == need) ans++;
if (j2 != j1 && i < j2 && j2 < k && H[j2] == need) ans++;
}
return ans;
}*/
/*void nen(vector<int>& H)
{
vector<int> temp = H;
sort(temp)
}*/
long long count_thdb(vector<signed> H)
{
int n = H.size();
vector<int> u(n), v(n);
for(int i = 0; i < n; i++)
{
u[i] = i - H[i];
v[i] = i + H[i];
}
}
long long count_triples(vector<int> H) {
int n = H.size();
long long count = 0;
for (int i = 0; i < n; i++) {
long long k = (long long)i + H[i];
if (k < n) {
if (H[i] > H[k]) {
int diff = H[i] - H[k];
int j1 = i + diff;
int j2 = i + H[k];
if (j1 > i && j1 < k && H[j1] == diff) {
count++;
}
if (j2 > i && j2 < k && j2 != j1 && H[j2] == diff) {
count++;
}
}
}
}
for (int k = 0; k < n; k++) {
long long i0 = (long long)k - H[k];
if (i0 >= 0) {
if (H[k] > H[i0]) {
int diff = H[k] - H[i0];
int j1 = i0 + H[i0];
int j2 = k - H[i0];
if (j1 > i0 && j1 < k && H[j1] == diff) {
count++;
}
if (j2 > i0 && j2 < k && j2 != j1 && H[j2] == diff) {
count++;
}
}
}
}
int MAXS = 2 * n + 10;
vector<vector<int>> list_A(MAXS + 1);
vector<vector<int>> list_sum(MAXS + 1);
for (int i = 0; i < n; i++) {
long long s = (long long)i + H[i];
if (s <= MAXS) {
list_A[s].push_back(i);
}
}
for (int k = 0; k < n; k++) {
long long s = (long long)k + H[k];
if (s <= MAXS) {
list_sum[s].push_back(k);
}
}
int B = sqrt(n);
for (int j = 0; j < n; j++) {
long long s = j;
if (s <= MAXS) {
for (int i : list_A[s]) {
if (i < j) {
long long k_val = (long long)i + H[j];
if (k_val < n) {
if (H[j] > H[i] && H[k_val] == H[j] - H[i]) {
count++;
}
}
}
}
}
long long s0 = (long long)j + H[j];
if (s0 > MAXS) continue;
long long low_bound = max((long long)j + 1, (long long)H[j]);
long long high_bound = min((long long)n - 1, (long long)j + H[j] - 1);
if (low_bound > high_bound) continue;
vector<int>& L = list_sum[s0];
if (L.empty()) continue;
if (L.size() <= (size_t)B) {
for (int k_val : L) {
if (k_val < low_bound) continue;
if (k_val > high_bound) break;
int i_val = k_val - H[j];
if (H[i_val] == k_val - j) {
count++;
}
}
} else {
for (int k_val = low_bound; k_val <= high_bound; k_val++) {
if (k_val + H[k_val] == s0) {
int i_val = k_val - H[j];
if (i_val >= 0 && i_val < j && H[i_val] == k_val - j) {
count++;
}
}
}
}
}
return count;
}
