#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
using lli = int64_t;
const int BLOCK_SIZE = 600;
long long count_triples(vector <int> H) {
int N = (int) H.size();
lli ans = 0;
for (int iter = 1; iter <= 2; ++iter) {
for (int i = 0; i < N; ++i) {
if (i < H[i]) continue;
int p = i - H[i];
if (H[p] >= H[i]) continue;
ans += H[p + H[p]] == H[i] - H[p];
if (H[i] != H[p] * 2) ans += H[i - H[p]] == H[i] - H[p];
}
reverse(H.begin(), H.end());
}
for (int i = 0; i < N; ++i) {
if (i + H[i] >= N) continue;
int j = i + H[i];
if (H[j] > H[i] and j + H[j] - H[i] < N) ans += H[j + H[j] - H[i]] == H[j] - H[i];
}
//j - i = H[j] - H[i]
//k - j = H[j] - H[k]
vector <vector <int>> lft_side(2 * N + 1), rht_side(2 * N + 1);
for (int i = 0; i < N; ++i) {
lft_side[i - H[i] + N].push_back(i);
}
for (int i = N - 1; i >= 0; --i) {
rht_side[i + H[i]].push_back(i);
}
//Small
for (int delta = 0; delta <= 2 * N; ++delta) {
vector <int>& list = lft_side[delta];
if ((int) list.size() > BLOCK_SIZE) continue;
int P = (int) list.size();
for (int i = 0; i < P; ++i) {
for (int j = i + 1; j < P; ++j) {
int x = list[i], y = list[j];
ans += x + H[y] < N and H[x + H[y]] == H[y] - H[x];
}
}
}
//Large
//k - i = H[i] + H[k];
for (int delta = 0; delta <= 2 * N; ++delta) {
if ((int) lft_side[delta].size() <= BLOCK_SIZE) continue;
vector <int> cnt(N + 1);
for (int j : lft_side[delta]) {
for (int k : rht_side[j + H[j]]) {
if (k <= j) break;
ans += k >= H[k] ? cnt[k - H[k]] : 0;
}
if (j + H[j] < N) cnt[j + H[j]] += 1;
}
}
for (int i = 0; i < N; ++i) {
if (H[i] % 2) continue;
int half_len = H[i] / 2;
ans -= i >= half_len and H[i - half_len] == half_len and i + half_len < N and H[i + half_len] == half_len;
}
return ans;
}
vector<int> construct_range(int M, int K) {
return {1, 1, 2};
}
