#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
const int nmax = 2e5 + 5;
int n;
unordered_map <int, vector <int>> mk;
ll count_triples(vector <int> H) {
n = H.size();
ll cnt = 0;
for (int j=0; j<n; j++) {
// Hj = j - i
int i = j - H[j];
if (i>=0) {
int k1 = i + H[i], k2 = j + H[i];
if (k1<n && k1>j && H[k1]==k1-j) cnt++;
if (k2<n && k2>j && H[k2]==k2-i) cnt++;
}
// Hj = k - j
int k = j + H[j];
if (k<n) {
int i1 = j - H[k], i2 = k - H[k];
if (i1>=0 && i1<j && H[i1]==k-i1) cnt++;
if (i2>=0 && i2<j && H[i2]==j-i2) cnt++;
}
mk[j - H[j]].push_back(j);
}
for (int i=0; i<n; i++) {
int j = i + H[i];
if (j<=n) {
int k = i + H[j];
if (H[k]==k-j) cnt++;
}
}
for (int i=0; i<n; i++) {
mk[i - H[i]].erase(remove(mk[i - H[i]].begin(), mk[i - H[i]].end(), i), mk[i - H[i]].end());
for (int k : mk[i + H[i]]) {
int j = H[i] + H[k];
if (j==k-i) cnt++;
}
}
return cnt;
}
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(2M, 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(2M, 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;
}
