#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
#define rep(i, n) for (int i = 0; i < (n); i++)
typedef long long ll;
#define pb push_back
#define st first
#define nd second
#define pii pair<int, int>
#define pll pair<ll, ll>
#define all(a) a.begin(), a.end()
set<pair<pii, int>> S;
pair<pii, int> sor(int a, int b, int c) {
int x = min({a, b, c});
int z = max({a, b, c});
int y = a + b + c - x - z;
return {{x, y}, z};
}
long long count_triples(std::vector<int> T) {
int n = T.size();
ll ans = 0;
rep(i, n) {
int j = i + T[i];
int k[4];
if (j < n) {
k[0] = i + T[j];
k[1] = i - T[j];
k[2] = j + T[j];
k[3] = j - T[j];
rep(c, 4) {
if (i == j || i == k[c] || j == k[c]) continue;
if (k[c] < 0 || k[c] >= n) continue;
int x = T[i];
int y = T[j];
int z = T[k[c]];
int a = abs(i - j);
int b = abs(i - k[c]);
int d = abs(j - k[c]);
if ((x + y + z) != (2 * max({x, y, z}))) continue;
if (sor(a, b, d) != sor(x, y, z)) continue;
S.insert(sor(i, j, k[c]));
}
}
j = i - T[i];
if (j >= 0) {
k[0] = i + T[j];
k[1] = i - T[j];
k[2] = j + T[j];
k[3] = j - T[j];
rep(c, 4) {
if (i == j || i == k[c] || j == k[c]) continue;
if (k[c] < 0 || k[c] >= n) continue;
int x = T[i];
int y = T[j];
int z = T[k[c]];
int a = abs(i - j);
int b = abs(i - k[c]);
int d = abs(j - k[c]);
if ((x + y + z) != (2 * max({x, y, z}))) continue;
if (sor(a, b, d) != sor(x, y, z)) continue;
S.insert(sor(i, j, k[c]));
}
}
}
ans = (long long) S.size();
// for (auto p: S) {
// cout << p.st.st << " " << p.st.nd << " " << p.nd << '\n';
// }
vector<int> jakie[2 * n + 1];
vector<int> jakie2[2 * n + 1];
int iter[n];
int iter2[n];
rep(i, n) {
int x = T[i] - i + n;
iter[i] = jakie[x].size();
jakie[x].pb(i);
}
for (int i = n - 1; i >= 0; i--) {
int x = T[i] + i;
iter2[i] = jakie2[x].size();
jakie2[x].pb(i);
}
rep(i, n) {
int x = T[i] - i + n;
int y = T[i] + i;
int sz = jakie[x].size();
int sz1 = jakie[y].size();
if (sz <= sz1) {
for (int it = iter[i] - 1; it >= 0; it--) {
int j = jakie[x][it];
int k = i + T[j];
if (k < n && ((T[k] + T[j]) == T[i])) {
S.insert(sor(i, j, k));
ans++;
}
}
}
else {
for (int it = iter2[i] - 1; it >= 0; it--) {
int k = jakie2[y][it];
int j = i - T[k];
if (j >= 0 && ((T[k] + T[j]) == T[i])) {
S.insert(sor(i, j, k));
ans++;
}
}
}
}
ans = S.size();
return ans;
}
std::vector<int> construct_range(int M, int K) {
return {1, 1, 1};
}
