#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
using vi = vector<int>;
using vvi = vector<vi>;
using vl = vector<ll>;
using vvl = vector<vl>;
using pi = pair<int, int>;
#define FOR(i, a, b) for (int i = a; i < b; i++)
#define ROF(i, a, b) for (int i = a; i >= b; i--)
#define each(a, x) for (auto &a : x)
#define all(x) (x).begin(), (x).end()
#define bg(x) (x).begin()
#define en(x) (x).end()
#define rev(x) reverse(all(x))
#define sz(x) int((x).size())
#define srt(x) sort(all(x))
#define cnt(a, x) count(all(x), a)
#define trace(x) each(a, (x)) cout << a << " "
#define mp make_pair
#define pb push_back
#define lb lower_bound
#define ub upper_bound
struct DSU {
int n; vi par, siz;
DSU() {};
DSU(int N) {
n = N; par.resize(n); siz.assign(n, 1);
iota(all(par), 0);
}
int find(int v) {
if (par[v] == v) return v;
return par[v] = find(par[v]);
}
void unite(int a, int b) {
a = find(a); b = find(b);
if (a != b) {
if (siz[a] < siz[b]) swap(a, b);
par[b] = a;
siz[a] += siz[b];
}
}
};
ll brute(vi h) {
int n = sz(h);
ll ans = 0;
// cerr << "brute function: \n";
FOR(i, 0, n) {
FOR(j, i+1, n) {
FOR(k, j+1, n) {
// vi d = {k - j, k - i, j - i}, f = {h[i], h[j], h[k]};
// srt(d); srt(f);
int d1 = min({k-j, k-i,j-i}), d3 = max({k-j, j-i, k-i});
int d2 = (k-j) ^ (k-i) ^ (j-i) ^ d1 ^ d3;
int f1 = min({h[i], h[j], h[k]}), f3 = max({h[i], h[j], h[k]});
int f2 = h[i] ^ h[j] ^ h[k] ^ f1 ^ f3;
// bool valid = d[0] == f[0] && d[1] == f[1] && d[2] == f[2];
// if (!valid) continue;
// ans++;
// cerr << i << " " << j << " " << k << "\n";
if (d1 == f1 && d2 == f2 && d3 == f3) ans++;
}
}
}
return ans;
}
struct Triple {
int i, j, k;
Triple() {};
Triple(int I, int J, int K) {
i = min({I, J, K});
k = max({I, J, K});
j = (I ^ J ^ K) ^ i ^ k; // lol
}
const bool operator<(const Triple &other) const {
if (i != other.i) return i < other.i;
if (j != other.j) return j < other.j;
return k < other.k;
}
};
ll increasing(vi h) {
int n = sz(h);
set<Triple> used;
FOR(i, 0, n) {
int k = i - h[i];
if (k < 0) continue;
int j1 = k + h[k], j2 = i - h[k];
if (k < j1 && j1 < i) {
int e = j1 + h[j1];
if (e == i) {
used.insert(Triple(i, j1, k));
}
}
if (k < j2 && j2 < i) {
int e = j2 - h[j2];
if (e == k) {
used.insert(Triple(i, j2, k));
}
}
}
// for (auto &el : used) {
// cerr << el.i << " " << el.j << " " << el.k << "\n";
// }
return sz(used);
}
ll count_triples(vi h) {
int n = sz(h);
ll ans = 0;
FOR(i, 0, n) {
FOR(j, 0, i) {
// for a given pair (i, j) the possible values for k are i - h[i], i - h[j], j+h[i], j+h[j]
int dist = i - j;
vi K = {i-h[i], i-h[j], j+h[i], j+h[j]};
set<int> seen;
each(k, K) {
if (!(j < k && k < i)) continue;
if (seen.count(k)) continue;
seen.insert(k);
vi d = {abs(i-j), abs(i-k), abs(j-k)}, f = {h[i], h[j], h[k]};
srt(d); srt(f);
bool valid = d[0] == f[0] && d[1] == f[1] && d[2] == f[2];
if (!valid) continue;
ans++;
// cerr << i << " " << j << " " << k << "\n";
}
}
}
return ans;
}
vi construct_range(int M, int K) {
return {1, 1, 2, 3, 3, 1, 2, 1, 4, 3, 2, 3, 1, 2, 1, 4, 3, 2, 3, 1};
}
