#include <bits/stdc++.h>
#include <iostream>
#include <vector>
#include <algorithm>
#include <cmath>
#include <iomanip>
#include <queue>
#include <random>
#include "triples.h"
using namespace std;
#define all(a) (a).begin(), (a).end()
#define ll long long
#define ld long double
#define ui uint64_t
#define cont(set, element) ((set).find(element) != (set).end())
#define pb push_back
#define chmin(x, y) (x = min(x, y))
#define chmax(x, y) (x = max(x, y))
/********* DEBUG *********/
template <typename T>
void outvec(const vector<T>& Z){
for (const T& x : Z)
cout << x << ' ';
cout << "\n";
}
void printVariable(const any& var) {
if (!var.has_value()) {
cout << "null";
return;
}
if (var.type() == typeid(int)) {
cout << any_cast<int>(var);
} else if (var.type() == typeid(double)) {
cout << any_cast<double>(var);
} else if (var.type() == typeid(float)) {
cout << any_cast<float>(var);
} else if (var.type() == typeid(char)) {
cout << any_cast<char>(var);
} else if (var.type() == typeid(bool)) {
cout << (any_cast<bool>(var) ? "true" : "false");
} else if (var.type() == typeid(string)) {
cout << any_cast<string>(var);
} else if (var.type() == typeid(const char*)) {
cout << any_cast<const char*>(var);
} else if (var.type() == typeid(long long)) {
cout << any_cast<long long>(var);
} else {
cout << "[unknown type]";
}
}
template<typename... Args>
void outval(Args... args) {
vector<any> variables = {args...};
for (size_t i = 0; i < variables.size(); ++i) {
printVariable(variables[i]);
if (i != variables.size() - 1) {
cout << " ";
}
}
cout << "\n";
}
/********* DEBUG *********/
#define sp << " " <<
#define fi first
#define se second
const ll MOD2 = 1e9 + 7;
const ll MOD = 998244353;
const ll inf = 1e18;
ll count_triples(vector<int> H) {
ll ans = 0, N = H.size();
unordered_map<ll, vector<ll>> seen;
unordered_set<ll> done;
// for hashing
ll mult = 200001;
auto add = [&](ll a, ll b, ll c) -> void {
vector<ll> vec = {a,b,c};
sort(all(vec));
ll hsh = vec[0] + vec[1] * mult + vec[2] * mult * mult;
done.insert(hsh);
};
for (int i = 0; i < H.size(); i++){
// middle value is detached, 2 cases
if (seen.count(i - H[i])){
for (auto &x : seen[i - H[i]]){
ll mid1 = x + H[x];
ll mid2 = x + H[i];
ll diff = i - x;
if (mid1 < N && H[mid1] == diff){
add(x, i, mid1);
}
if (mid1 != mid2 && mid2 < N && H[mid2] == diff){
add(x, i, mid2);
}
}
}
seen[H[i] + i].pb(i);
// GO FRONT
ll frontIndex = H[i] + i;
if (frontIndex < N){
ll middleIndex = frontIndex - H[frontIndex];
if (middleIndex >= 0 && middleIndex - H[middleIndex] == i){
add(i, middleIndex, frontIndex);
}
middleIndex = i + H[frontIndex];
if (middleIndex < N && middleIndex + H[middleIndex] == frontIndex){
add(i, middleIndex, frontIndex);
}
if (middleIndex < N && middleIndex - H[middleIndex] == frontIndex){
add(i, middleIndex, frontIndex);
}
ll moreFrontIndex = frontIndex + H[frontIndex];
if (moreFrontIndex < N && moreFrontIndex - H[moreFrontIndex] == i){
add(i, frontIndex, moreFrontIndex);
}
}
ll backIndex = i - H[i];
if (backIndex < 0)
continue;
// go back immediately, 3 cases
ll middleIndex = backIndex + H[backIndex];
if (middleIndex < N && middleIndex + H[middleIndex] == i){
add(i, middleIndex, backIndex);
}
middleIndex = i - H[backIndex];
if (middleIndex >= 0 && middleIndex - H[middleIndex] == backIndex){
add(i, middleIndex, backIndex);
}
if (middleIndex >= 0 && middleIndex + H[middleIndex] == backIndex){
add(i, middleIndex, backIndex);
}
// extend even more, 1 case
ll moreBackIndex = backIndex - H[backIndex];
if (moreBackIndex >= 0 && moreBackIndex + H[moreBackIndex] == i){
add(i, backIndex, moreBackIndex);
}
}
return done.size();
}
std::vector<int> construct_range(int M, int K) {
return {1, 1, 1};
}
