#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
vector<int> h;
vector<bool> vis;
bool check_range(int i, int j, int k) {
// checks if the range is correct and H[i] is the lowest
if(vis[i] || vis[j] || vis[k]) return false;
if(i < 0LL || j < 0LL || k < 0LL || k < j) return false;
if(i >= h.size() || j >= h.size() || k >= h.size()) return false;
vector<long long> diff = {abs(i - j), abs(i - k), abs(j - k)};
vector<long long> diff2 = {h[i], h[j], h[k]};
sort(diff.begin(), diff.end());
sort(diff2.begin(), diff2.end());
return diff == diff2;
}
long long count_triples(std::vector<int> H) {
h = H;
long long ans = 0;
int n = h.size();
vector<pair<int, int> > h_sizes;
vis.resize(n);
for(int i = 0; i < n; i++) {
h_sizes.push_back({h[i], i});
vis[i] = false;
}
sort(h_sizes.begin(), h_sizes.end());
for(int i = 0; i < h_sizes.size(); i++) {
int idx = h_sizes[i].second;
for(int j = 0; j < n; j++) {
int this_diff = abs(idx - j);
int actual_diff = (h_sizes[i].first == this_diff) ? h[j] : h_sizes[i].first;
ans += check_range(idx, j, j - actual_diff);
// if(check_range(idx, j, j - actual_diff)) cout << "1: " << idx << " " << j << " " << j - actual_diff << "\n";
ans += check_range(idx, j, j + actual_diff);
// if(check_range(idx, j, j + actual_diff)) cout << "2: " << idx << " " << j << " " << j + actual_diff << "\n";
ans += check_range(idx, j, idx - actual_diff);
// if(check_range(idx, j, idx - actual_diff)) cout << "3: " << idx << " " << j << " " << i - actual_diff << "\n";
ans += check_range(idx, j, idx + actual_diff);
// if(check_range(idx, j, idx + actual_diff)) cout << "4: " << idx << " " << j << " " << i + actual_diff << "\n";
}
vis[idx] = true;
}
return ans;
}
std::vector<int> construct_range(int M, int K) {
// std::mt19937_64 RNG(std::chrono::steady_clock::now().time_since_epoch().count());
// std::vector<int> peak_range;
// for(int i = 0; i < M; i++) {
// peak_range.push_back(RNG() % 10 + 5);
// }
// return peak_range;
return {};
}
