//#include "worldmap.h"
#include "triples.h"
#include <bits/stdc++.h>
#pragma GCC optimize("Ofast")
#pragma GCC target("sse2")
#define ll long long
#define db double
#define ld long double
#define endl '\n'
#define eb emplace_back
#define em emplace
#define pb push_back
#define pf push_front
#define pp pop_back
#define fr first
#define sc second
#define sz size
#define ir insert
#define yes cout << "YES" << endl
#define no cout << "NO" << endl
#define all(x) x.begin() , x.end()
#define alice cout << "Alice" << endl
#define bob cout << "Bob" << endl
#define fo(x , y) for(ll i = x;i < y;i++)
using namespace std;
mt19937 rd(time(NULL));
//IOI 2025 problems
const ll mxn = 1e5+5;
const ll md=998244353;
//vector<int> g[mxn];
/* "souvenirs" -> 39 points for now
void buy_souvenirs(int N, ll P0) {
if(N==2){transaction(P0-1) ;return;}
if(N==3){
auto x=transaction(P0-1);
if(x.fr.sz()==1){ll vl=P0-1-x.sc; transaction(vl-1);transaction(vl-1);}
else{ll vl= (P0-1-x.sc) ; vl+=(2-vl%2)%2;vl/=2; transaction(vl-1);}
return;
}
vector<ll>cn(N,0) , vl(N);
vl[0]=P0;
for(int i =1;i < N;i++) {
auto x =transaction(vl[i-1] - 1) ;
for(int y: x.fr) cn[y]++;
if(x.fr.sz() ==1) vl[i] = vl[i-1] - 1 -x.sc;
else vl[i] = vl[i-1] - 2;
}
for(int i = 1; i<N;i++) {
while(cn[i] <i) {
transaction(vl[i]);
cn[i]++;
}
}
}
*/
/* "World Map" -> 72 points for now
vector<vector<int>> regulate(vector<vector<int>> board) {
int n= board.sz();
int m=board[0].sz() ;
int k = max(n,m);
vector an=vector(k,vector<int> (k));
for(int i=0;i<n;i++)for(int j = 0;j<m ;j++)an[i][j]=board[i][j];
for(int i=0;i<k;i++){for(int j=0;j<k;j++){
if(!an[i][j]){
if(j>0&&an[i][j-1])an[i][j] =an[i][j-1];
else if(i>0&&an[i-1][j]) an[i][j] =an[i-1][j];
else assert(false);
}
}}
return an;
}
bool vs[mxn] ;
vector<pair<int, bool>> st;
void dfs(int v, int pa=-1) {
vs[v]=true;
for(int u:g[v]) {
if(vs[u])continue;
st.pb({u,true});
dfs(u,v);
st.pb({v,false});
}
}
vector<vector<int>> create_map(int N, int M , vector<int> A , vector<int> B) {
for(int i = 1 ; i <= N ;i++) g[i].clear();
fill(vs,vs + N+1, false) ;
for(int i = 0 ;i < M;i++){g[A[i]].pb(B[i]) ;g[B[i]].pb(A[i]);}
st=vector<pair<int,bool>>{{1,true}};
dfs(1);
vector ans=vector(N*3 +(N-1), vector<int> (N*2)) ;
int x= 0;
for(auto [v,fi]:st) {
if(fi) {
for(int j=0;j<3;j++){for(int k = 0; k < N*2;k++)ans[x+j][k]=v;}
for(int j =0;j <g[v].sz() ;j++)ans[x+1][j*2] = g[v][j];
x+=3;
}
else{
for(int k =0;k<N*2;k++)ans[x][k]=v;
x++;
}
}
return regulate(ans) ;
}
*/
//"Triple Peaks" , goal -> 50
set<tuple<int, int , int>> sn;
inline bool works(int i , int j , int k , const vector<int> &H){
int p[3] = {i , j , k};
sort(p , p +3);
i = p[0] , j = p[1] , k =p[2];
if(0>i||i >=j || j >=k || k >=H.sz()) return false;
if(j-i == H[k] && k - j == H[i]) return false;
if(sn.count({i,j,k})) return false;
int d[3] = {j - i , k - j , k -i};
int h[3] = {H[i] , H[j] ,H[k]} ;
sort(d , d+3);
sort(h, h+3);
if(d[0]==h[0] && d[1] == h[1] && d[2] == h[2]) {sn.em(i , j , k); return true;}
return false;
}
struct comb{
map<int, int> a;
ll operator*(const comb& b)const{
if(a.sz() > b.a.sz()) return b * *this;
ll o=0;
for(auto [i,v] :a) if(b.a.count(i)) o+=(ll)v*b.a.at(i);
return o;
}
void insert(int v){a[v]++;}
void remove(int v) {if(!--a[v]){a.erase(v);}}
};
ll count_triples(vector<int> H) {
cerr << "count_triples(...)\n";
const int N = H.sz();
ll ct=0;
vector<int> xm(N) , xp(N);
for(int x = 0 ; x< N ; x++) {xm[x]=x-H[x]; xp[x] =x+H[x];}
map<int, comb>lf, rt;
for(int i =0 ; i < N;i++)rt[xp[i]].insert(xm[i]);
for(int j = 0 ; j < N;j++){
rt[xp[j]].remove(xm[j]);
ct += lf[xm[j]] * rt[xp[j]];
lf[xm[j]].insert(xp[j]);
}
cerr<<"pre-trivial: "<< ct<< endl;
for(int i =0 ; i <N;i++){
for(int j :{i + H[i], i-H[i]}){
if(j < 0||j>=N)continue;
for(int k :{i+H[j], i-H[j], j+H[j],j-H[j]}) ct+=works(i , j , k , H);
}
}
cerr<< " = "<<ct<<endl;
return ct;
}
vector<int> construct_range(int M , int K) {
return {};
}
