#include <bits/stdc++.h>
using namespace std;
#define nl "\n"
#define nf endl
#define ll long long
#define pb push_back
#define _ << ' ' <<
#define INF (ll)1e18
#define mod 998244353
#define maxn 50010
#include "triples.h"
long long count_triples(std::vector<int> H) {
// subtask 5
ll n = H.size();
vector<array<ll, 3>> triples;
auto match = [&](ll i, ll j, ll k) {
// cout << "match" _ i _ j _ k << nf;
if (-1 >= i || i >= j || j >= k || k >= n) return;
if (H[i] == k - j && H[j] == k - i && H[k] == j - i) return;
array<ll, 3> a = {j - i, k - j, k - i};
array<ll, 3> b = {H[i], H[j], H[k]};
sort(a.begin(), a.end());
sort(b.begin(), b.end());
if (a == b) triples.pb({i, j, k});
};
// H[k] = k - i
for (ll k = 0; k < n; k++) {
ll i = k - H[k];
if (i < 0) continue;
ll hj = 2 * k - 2 * i - H[i] - H[k];
{
ll j = k - hj;
match(i, j, k);
}
{
ll j = i + hj;
match(i, j, k);
}
}
// H[k] = k - j
for (ll k = 0; k < n; k++) {
ll j = k - H[k];
if (j < 0) continue;
{
ll i = k - H[j];
match(i, j, k);
}
{
ll i = j - H[j];
match(i, j, k);
}
}
// H[k] = j - i, H[i] = k - i
map<ll, vector<ll>> by_k;
for (ll i = 0; i < n; i++) by_k[H[i] + i].pb(i);
for (ll k = 0; k < n; k++) {
for (auto i : by_k[k]) {
ll j = i + H[k];
match(i, j, k);
}
}
sort(triples.begin(), triples.end());
triples.resize(unique(triples.begin(), triples.end()) - triples.begin());
ll ans = triples.size();
// bad case
map<ll, bitset<maxn>> im, ip;
for (ll i = 0; i < n; i++) {
ip[i + H[i]][i] = 1;
}
for (ll j = 0; j < n; j++) {
ip[j + H[j]][j] = 0;
auto bt = im[j - H[j]] & (ip[j + H[j]] >> H[j]);
ans += bt.count();
/* for (ll i = 0; i < 20; i++) cout << bt[i];
cout << nl; */
im[j - H[j]][j] = 1;
}
return ans;
}
std::vector<int> construct_range(int M, int K) {
vector<ll> v = {3, 1, 2, 1, 4, 3, 2, 3, 1, 5, 1, 3, 2, 3, 4, 1, 2, 1, 3};
vector<int> ans;
for (ll i = 0; i < M; i++) ans.pb(v[i % v.size()]);
return ans;
}
