#pragma GCC optimize ("O3")
#include "triples.h"
using namespace std;
#include <bits/stdc++.h>
#define rep(i,a,b) for(int i = a; i < b; i++)
long long count_triples(std::vector<int> arr) {
int n = arr.size();
auto valid = [&](int i, int j, int k) {
if (!(i < j && j < k)) return false;
int a[3] = {j-i, k-i, k-j};
int b[3] = {arr[i], arr[j], arr[k]};
return (
(a[0] == b[0] && a[1] == b[1] && a[2] == b[2]) ||
(a[0] == b[0] && a[1] == b[2] && a[2] == b[1]) ||
(a[0] == b[1] && a[1] == b[0] && a[2] == b[2]) ||
(a[0] == b[1] && a[1] == b[2] && a[2] == b[0]) ||
(a[0] == b[2] && a[1] == b[0] && a[2] == b[1]) ||
(a[0] == b[2] && a[1] == b[1] && a[2] == b[0])
);
};
set<tuple<int,int,int>> ans_s;
rep(i,0,n) {
for (auto j : {i - arr[i], i + arr[i]}) {
if (j < 0 || j > n-1) continue;
for (auto k : {j - arr[j], j + arr[j], i - arr[j], i + arr[j]}) {
if (k < 0 || k > n-1) continue;
if (i == j || i == k || j == k) continue;
int x[] = {i, j, k};
sort(x, x+3);
if (valid(x[0], x[1], x[2])) ans_s.insert({x[0],x[1],x[2]});
}
}
}
vector<int> valid_before(n, 0);
vector<vector<int>> cand_before(2*n), cand_after(2*n);
vector<int> before_cnt(n, 0), after_cnt(n, 0);
rep(b,0,n) {
before_cnt[b] = cand_before[arr[b]-b+n].size();
cand_before[arr[b]-b+n].push_back(b);
}
for (int b = n-1; b >= 0; b--) {
after_cnt[b] = cand_after[arr[b]+b].size();
cand_after[arr[b]+b].push_back(b);
}
rep(b,0,n) {
if (before_cnt[b] < after_cnt[b]) {
rep(i,0,before_cnt[b]) {
int a = cand_before[arr[b]-b+n][i];
int c = a + arr[b];
if (valid(a, b, c)) ans_s.insert({a, b, c});
}
}
else {
rep(i,0,after_cnt[b]) {
int c = cand_after[arr[b]+b][i];
int a = c - arr[b];
if (valid(a, b, c)) ans_s.insert({a, b, c});
}
}
}
for (auto [a, b, c] : ans_s) {
assert(valid(a, b, c));
}
int ans = ans_s.size();
return ans;
}
std::vector<int> construct_range(int M, int K) {
vector<int> res(M);
rep(i,0,M) res[i] = 1 + (rand() % (M-1));
rep(iter,0,100) {
int i = rand() % M;
for (int j = 0; j < res[i]; j++) {
if (i + j < M) {
if (rand() % 5) res[i+j] = res[i] - j;
}
if (i - j >= 0) {
if (rand() % 5) res[i-j] = res[i] - j;
}
}
}
return res;
}
