#include <iostream>
#include <vector>
#include <algorithm>
#include <unordered_set>
#include <set>
using namespace std;
int64_t pack(int i, int j, int k) {
return ((int64_t)i << 40) | ((int64_t)j << 20) | ((int64_t)k);
}
void check(int i, int j, int k, vector<int>&a \
, unordered_set<int64_t> &s) {
vector<int> x = { j - i, k - i, k - j };
vector<int> y = { a[i], a[j], a[k] };
sort(x.begin(), x.end());
sort(y.begin(), y.end());
for (int i = 0; i < 3; ++i)
if (x[i] != y[i]) return;
s.insert(pack(i, j, k));
}
void findi(int j, int k, vector<int>&a \
, unordered_set<int64_t> &ms) {
if ((k < 0) || ((k >= a.size()))) return;
if ((j < 0) || ((j >= a.size()))) return;
vector<int> op = { j - a[j],
k - a[k], j - a[k], k - a[j] };
sort(op.begin(), op.end());
op.erase(unique(op.begin(), op.end()), op.end());
for (auto i : op)
if ((i >= 0) && (i < a.size()))
if ((k + a[k]) == (j + a[j]))
check(i, j, k, a, ms);
}
void findk(int i, int j, vector<int>& a \
, unordered_set<int64_t> &ms) {
if ((j < 0) || ((j >= a.size()))) return;
if ((i < 0) || ((i >= a.size()))) return;
vector<int> op = { i + a[i],
j + a[i], i + a[j], j + a[j] };
sort(op.begin(), op.end());
op.erase(unique(op.begin(), op.end()), op.end());
for (auto k : op)
if ((k >= 0) && (k < a.size()))
if ((k + a[k]) == (j + a[j]))
check(i, j, k, a, ms);
}
long long count_triples(vector<int> &a) {
unordered_set<int64_t> ans;
int n = a.size();
ans.reserve(max(1, n * 2));
for (int x = 0; x < n; ++x)
for (auto y : { x - a[x], x + a[x]})
if (!((y < 0) || ((y >= a.size())))) {
vector<int> op = { x - a[x], x + a[x], y + a[y], y - a[y],
y + a[x], y - a[x], x + a[y], x - a[y] };
sort(op.begin(), op.end());
op.erase(unique(op.begin(), op.end()), op.end());
for (auto z : op) {
if ((z < 0) || ((z >= a.size()))) continue;
vector<int> op = { x, y, z };
sort(op.begin(), op.end());
check(op[0], op[1], op[2], a, ans);
}
}
vector<vector<int>> x(n + n), y(n + n);
for (int i = 0; i < n; ++i)
x[a[i] - i + n].push_back(i);
for (int i = 0; i < n; ++i)
y[a[i] + i].push_back(i);
for (int j = 0; j < n; ++j) {
if (x[a[j] - j + n].size() < y[a[j] + j].size())
for (auto i : x[a[j] - j + n])
findk(i, j, a, ans);
else
for (auto k : y[a[j] + j])
findi(j, k, a, ans);
}
return (int)ans.size();
}
vector<int> construct_range(int M, int K) {
vector<int> a = { 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19 }; return a;
}
//int main() { vector<int> a = { 4, 1, 4, 3, 2, 6, 1 }; cout << count_triples(a); }
