#include "triples.h"
#include <bits/stdc++.h>
#ifdef LOCAL
#include "Debug.h"
#else
#define debug(...) 42
#endif
using namespace std;
long long calc(vector<int> h)
{
int n = size(h);
vector<int> l(n), r(n);
vector<vector<int>> lAt(n * 3), rAt(n * 3);
for (int i = 0; i < n; i++)
{
l[i] = i - h[i];
lAt[l[i] + n].push_back(h[i]);
r[i] = i + h[i];
rAt[r[i] + n].push_back(h[i]);
}
for (int i = 0; i < n * 3; i++)
{
sort(begin(lAt[i]), end(lAt[i]));
sort(begin(rAt[i]), end(rAt[i]));
}
long long res = 0;
for (int i = 0; i < n; i++)
{
int j = r[i];
if (j < n)
{
// 2.3..5
res += r[j] < n && h[r[j]] == h[i] + h[j];
// 2.5..3
if (h[j] > h[i])
{
int k = j + h[j] - h[i];
if (k < n && l[k] == j)
res++;
}
// 5.3..2
if (h[j] < h[i])
{
int k = i + h[j];
if (r[k] == j && h[k] != h[j]) // exclude 211
res++;
}
}
// k.2..5.3..j
int ll = l[i] + n, rr = r[i] + n, szL = size(lAt[ll]), szR = size(rAt[rr]);
for (int u = 0, v = szR - 1; u < szL && v >= 0;)
if (lAt[ll][u] + rAt[rr][v] == h[i])
{
res += lAt[ll][u] != rAt[rr][v];
u++;
}
else if (lAt[ll][u] + rAt[rr][v] < h[i]) u++;
else v--;
}
for (int i = 0; i < n; i++)
{
int j = l[i];
if (j < 0)
continue;
// 5.2..3
if (l[j] >= 0 && h[l[j]] == h[i] + h[j])
res++;
// 3.2..5
int k = i + h[j];
if (r[j] != i && k < n && h[k] == h[i] + h[j]) // exclude 112
res++;
}
return res;
}
long long count_triples(vector<int> h) {
return calc(h);
}
vector<int> construct_range(int M, int K) {
return {1, 1, 1};
}
