//#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
vector<int> construct_range(int M , int K) {
vector<int> rs(M , 0) ;
for(int i =0;i<M ;i++) {rs[i] = 1 ; if(i%3 ==2) rs[i] = 2;}
return rs;
}
ll count_triplesnd(vector<int> H) {
int N = H.sz() ;
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;
}
ll count_triples(vector<int> H) {
int n=H.sz() , b=0;
bool cz = true;
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]) cz =false;
if(cz) 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;
}
