#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
using ld = long double;
#define fi first
#define se second
#define vi vector<int>
#define vll vector<long long>
#define pii pair<int, int>
#define pll pair<long long, long long>
#define pb push_back
#define mp make_pair
#define eb emplace_back
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)(x).size()
mt19937 rng(chrono::high_resolution_clock::now().time_since_epoch().count());
mt19937_64 rng64(chrono::high_resolution_clock::now().time_since_epoch().count());
inline int rand(int l,int r){return uniform_int_distribution<int>(l, r)(rng);}
inline ll rand(ll l,ll r){return uniform_int_distribution<ll>(l, r)(rng64);}
#ifdef DEBUG
auto&operator<<(auto&o,pair<auto,auto>p){return o<<"("<<p.first<<", "<<p.second<<")";}
auto operator<<(auto&o,auto x)->decltype(x.end(),o){o<<"{";int i=0;for(auto e:x)o<<","+!i++<<e;return o<<"}";}
#define debug(X...)cerr<<"["#X"]: ",[](auto...$){((cerr<<$<<"; "),...)<<endl;}(X)
#else
#define debug(...){}
#endif
struct custom_hash {
static uint64_t splitmix64(uint64_t x) {
x += 0x9e3779b97f4a7c15;
x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
return x ^ (x >> 31);
}
size_t operator()(uint64_t x) const {
static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
return splitmix64(x + FIXED_RANDOM);
}
};
struct pair_hash{
size_t operator()(const pair<int,int>&x)const{
return hash<long long>()(((long long)x.first)^(((long long)x.second)<<32));
}
};
const int B = 369;
ll count_triples(vi H){
ll ans = 0LL;
int n = sz(H);
vector<vi> vec(2 * n + 1, vi());
for(int i = 0; i < n; i++){
if(i + H[i] < n && H[i + H[i]] > H[i] && i + H[i + H[i]] < n && H[i + H[i + H[i]]] == H[i + H[i]] - H[i]){
ans++;
}
if(i + H[i] < n && H[i + H[i]] < H[i]){
if(H[i + H[i + H[i]]] == H[i] - H[i + H[i]]){
ans++;
}
if(H[i + H[i] - H[i + H[i]]] == H[i] - H[i + H[i]] && i + H[i] - H[i + H[i]] != i + H[i + H[i]]){
ans++;
}
}
if(i - H[i] >= 0 && H[i - H[i]] < H[i]){
if(H[i - H[i - H[i]]] == H[i] - H[i - H[i]]){
ans++;
}
if(H[i - H[i] + H[i - H[i]]] == H[i] - H[i - H[i]] && i - H[i] + H[i - H[i]] != i - H[i - H[i]]){
ans++;
}
}
vec[H[i] - i + n].pb(i);
}
for(int x = 0; x < 2 * n + 1; x++){
if(sz(vec[x]) > B){
int X = x - n;
for(int k = 0; k < n; k++){
if((k - H[k] - X) & 1){
continue;
}
int i = (k - H[k] - X) / 2;
int j = H[k] + i;
if(i < j && j < k && H[i] - i == X && H[j] - j == X){
ans++;
}
}
}else{
for(int i = 0; i < sz(vec[x]); i++){
for(int j = i + 1; j < sz(vec[x]); j++){
if(H[vec[x][j]] > H[vec[x][i]] && H[vec[x][j]] - H[vec[x][i]] == H[vec[x][i] + H[vec[x][j]]]){
ans++;
}
}
}
}
}
return ans;
}
vi construct_range(int M, int K){
return {1, 1, 1};
}
