#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<vector <int> ,ll> pvl;
#define st first
#define nd second
vector <int> rek(int N)
{
if(N == 0)return {};
if(N == 1)return {1};
if(N == 2)return {1,1};
if(N%3 != 2)
{
vector <int> temp = rek(N-1); temp.push_back(1);
return temp;
}
vector <int > r;
int s1 = N/3 ;
int s2 = s1+N/3+1;
vector <int> temp = rek((N/3));
for(auto p : temp)r.push_back(p);
r.push_back(N/3+1);
for(auto p : temp)r.push_back(N/3+1-p);
r.push_back(N/3+1);
for(auto p : temp)r.push_back(p);
return r;
}
vector<int> construct_range(int M, int K)
{
if(M == 0)return {};
if(M == 1)return {1};
int pot = 1;
while(pot < M)pot *= 3;
pot /= 3;
vector <int> res = rek(pot);
M -= res.size();
vector <int> temp = construct_range(M,K);
for(auto p : temp)res.push_back(p);
return res;
}
long long count_triplesnd(vector<int> H)
{
int N = H.size();
ll ile = 0;
for(int i = N-1 ; i >= 0 ; i--)
{
int k = i-H[i];
if(k < 0)continue;
int j = k+H[k];
if(j < 0 || j >= N);
else if(H[k]+H[j] == H[i] && (i-j) == H[j] && k < j && j < i)ile++;
j = i-H[k];
if(k+H[k] == j)continue;
if(j < 0 || j >= N);
else if(H[k]+H[j] == H[i] && (j-k) == H[j] && k < j && j < i)ile++;
}
return ile;
}
long long count_triples(vector<int> H)
{
int N = H.size();
int B = 0;
bool czynd = 1;
for(int i = 0; i < N ; i++)B = max(B , H[i]);
for(int i = 1; i < N ; i++)
{
if(H[i-1] > H[i])czynd = 0;
}
if(czynd)return count_triplesnd(H);
ll ile = 0;
for(int i = 0 ; i < N ; i++)
{
for(int j = i+1 ; j < min(N,i+B+1) ; j++)
{
int d = j-i;
if(H[i] == d || H[j] == d)
{
int R = 0;
if(H[i] == d)R = H[j];
else R = H[i];
int k = j+R;
if(k >= 0 && k < N && k > j && H[k] == R+d)ile++;
k = i+R;
if(k >= 0 && k < N && k > j && R == H[k]+d)ile++;
}
else
{
int k = j+min(H[i] , H[j]);
if(k >= 0 && k < N && H[k] == d && min(H[i],H[j])+d == max(H[i],H[j]))ile++;
}
}
}
return ile;
}
