#include <bits/stdc++.h>
#include "triples.h"
using namespace std;
typedef long long ll;
const int N = 200000;
ll ans;
int n;
int a[N], c[N];
void print(ll x, char sep = ' '){
cout << x << sep;
}
bool check(int i, int j, int k){
c[k - j]++, c[j - i]++, c[k - i]++, c[a[i]]--, c[a[j]]--, c[a[k]]--;
if(!c[k - j] && !c[j - i] && !c[k - i]) return 1;
c[k - j] = c[j - i] = c[k - i] = c[a[i]] = c[a[j]] = c[a[k]] = 0;
return 0;
}
ll count_triples(vector < int > h){
n = h.size(), ans = 0;
map < vector < int >, bool > was;
for(int i = 0; i < n; i++) a[i] = h[i];
for(int i, k, j = 0; j < n; j++){
i = j - a[j];
if(i >= 0){
k = i + a[i];
if(k < n && j < k && check(i, j, k) && !was[{i, j, k}]) ans++, was[{i, j, k}] = 1;
k = j + a[i];
if(k < n && j < k && check(i, j, k) && !was[{i, j, k}]) ans++, was[{i, j, k}] = 1;
}
k = j + a[j];
if(k < n){
i = k - a[k];
if(i >= 0 && i < j && check(i, j, k) && !was[{i, j, k}]) ans++, was[{i, j, k}] = 1;
i = j - a[k];
if(i >= 0 && i < j && check(i, j, k) && !was[{i, j, k}]) ans++, was[{i, j, k}] = 1;
}
}
for(int i = 0; i < n; i++){
int j = i + a[i], k = i + a[a[i] + i];
if(a[j] == k - i && a[k] == k - j && a[i] == j - i){
if(0 <= i && i < j && j < k && k < n && check(i, j, k) && !was[{i, j, k}]) ans++, was[{i, j, k}] = 1;
}
}
for(int j = 0; j < n; j++){
for(int i = 0; i < j; i++){
int k = i + a[j];
if(a[j] == k - i && a[i] == k - j && a[k] == j - i && k + i != 2 * j){
if(0 <= i && i < j && j < k && k < n && check(i, j, k)) ans++;
}
}
}
//1)
// a[j] = k - i -> i + a[a[i] + i] = k
// a[i] = j - i -> a[i] + i = j
// a[k] = k - j -> a[k] - k = j
//2)
// a[j] = k - i -> a[j] = a[i] + j - i -> a[j] - j = a[i] - i
// a[i] = k - j -> a[i] + j = k
// a[k] = j - i -> a[k] = a[i] + a[j]
// a[a[i] + j] = a[i] + a[j] && a[j] - j == a[i] - i
return ans;
}
vector < int > construct_range(int n, int k){
vector < int > v;
n /= 5;
while(n--) v.push_back(1), v.push_back(1), v.push_back(2), v.push_back(2), v.push_back(3);
return v;
}
