#include "triples.h"
#include<bits/stdc++.h>
using namespace std;
int n;
long long rez = 0;
map<tuple<int,int,int>,int> mp;
vector<int> h;
void add(int i, int j, int k)
{
if(i >= j || j >= k)
return;
if(i < 0 || k >= n)
return;
if(h[k] == j-i && h[i] == k-j && h[j] == k-i) return;///caz special----------------------------------------------
vector<int> v1 = {j-i,k-j,k-i};
vector<int> v2 = {h[i],h[j],h[k]};
sort(v1.begin(),v1.end());
sort(v2.begin(),v2.end());
//if(min(j-i, k-j) == min({h[i],h[j],h[k]}) && k-i == max({h[i],h[j],h[k]}) && h[i] + h[j] + h[k] == 2 * max({h[i],h[j],h[k]}))
if(v1 == v2)
{
if(mp[{i,j,k}] == 0)
rez++;
mp[{i,j,k}] = 1;
}
}
vector<int> ofval[400005][2];
long long count_triples(std::vector<int> H)
{
h = H;
n = h.size();
for(int j=0;j<n;j++)
{
if(j - h[j] >= 0) add(j - h[j], j, (j - h[j]) + h[j - h[j]]);
if(j - h[j] >= 0) add(j - h[j], j, j + h[j - h[j]]);
if(j + h[j] < n) add(j - h[j + h[j]], j, j + h[j]);
if(j + h[j] < n) add((j + h[j]) - h[j + h[j]], j, j + h[j]);
}
for(int i=0;i<n;i++)
{
int j = i + h[i];
if(j < n) add(i, j, i + h[j]);
}
for(int i=0;i<n;i++)
{
ofval[i + h[i]][0].push_back(i);
ofval[i - h[i] + n][1].push_back(i);
}
for(int j=0;j<n;j++)
{
if(ofval[j + h[j]][0].size() <= ofval[j - h[j] + n][1].size())
{
for(int k:ofval[j + h[j]][0])
{
int i = j - h[k];
if(i < j && j < k && i >= 0 && k < n && h[k] == j-i && h[i] == k-j && h[j] == k-i)
rez++;
}
}
else
{
for(int i:ofval[j - h[j] + n][1])
{
int k = j + h[i];
if(i < j && j < k && i >= 0 && k < n && h[k] == j-i && h[i] == k-j && h[j] == k-i)
rez++;
}
}
}
return rez;
}
std::vector<int> construct_range(int M, int K)
{
return {};
}
