#include <bits/stdc++.h>
using namespace std;
using ll = long long;
//sub4:
std::vector<int> construct_range(int M, int K)
{
return{};
}
/*long long count_triples(vector<int> H)
{
int n = H.size();
ll ans = 0;
for (int k = 0; k < n; k++)
{
int c = H[k];
int i = k - c;
if (i < 0 || i >= n) continue;
int a = H[i];
if (a > c - a) continue;
int need = c - a;
int j1 = i + a;
int j2 = k - a;
if (i < j1 && j1 < k && H[j1] == need) ans++;
if (j2 != j1 && i < j2 && j2 < k && H[j2] == need) ans++;
}
return ans;
}*/
ll count_triples(vector<int> H)
{
int N = H.size();
ll ans = 0;
for (int i = 0; i < N; i++)
{
int k = i + H[i];
if (k >= N) continue;
// if H[k] == j - i → j = i + H[k]
{
int j = i + H[k];
if (j > i && j < k && H[j] == k - j)
ans++;
}
// if H[k] == k - j → j = k - H[k]
{
int j = k - H[k];
if (j > i && j < k && H[j] == j - i)
ans++;
}
}
for (int k = 0; k < N; k++)
{
int i = k - H[k];
if (i < 0) continue;
{
int j = i + H[i];
if (j > i && j < k && H[j] == k - j)
ans++;
}
{
int j = k - H[i];
if (j > i && j < k && H[j] == j - i)
ans++;
}
}
for (int i = 0; i < N; i++)
{
int j = i + H[i];
if (j >= N) continue;
int k = i + H[j];
if (k < N && H[k] == k - j)
ans++;
}
int T = int(sqrt(N));
vector<vector<int>> groups(2*N+1);
for (int i = 0; i < N; i++)
{
int x = H[i] - i + N;
groups[x].push_back(i);
}
for (int gx = 0; gx <= 2*N; gx++)
{
auto &vec = groups[gx];
if (vec.empty()) continue;
int C = gx - N;
if ((int)vec.size() <= T)
{
for (int a = 0; a < (int)vec.size(); a++)
{
for (int b = a+1; b < (int)vec.size(); b++)
{
int i = vec[a], j = vec[b];
int k = i + j + C;
if (k < N && j < k && H[k] == j - i)
ans++;
}
}
}
else
{
for (int k = 0; k < N; k++)
{
int sum = k - C;
int diff = H[k];
if (((sum + diff) & 1) != 0) continue;
int j = (sum + diff) >> 1;
int i = j - diff;
if (0 <= i && i < j && j < k)
{
if (H[i] - i == C && H[j] - j == C) ans++;
}
}
}
}
return ans;
}
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