#include "bits/stdc++.h"
using namespace std;
using ll = long long;
using ld = long double;
using ull = unsigned long long;
ll res = 0;
void add(ll i, ll j, ll k) {
// cout << "Debug: " << i << ' ' << j << ' ' << k << endl;
res ++;
}
long long countr(const vector<int> &a, const vector<int> &b) {
int n = (int)a.size();
if (n == 0) return 0;
int T = max(1, (int)std::sqrt((double)n));
vector<vector<int>> posA(n);
for (int i = 0; i < n; ++i) posA[a[i]].push_back(i);
vector<tuple<int,int,int>> triples;
triples.reserve(n);
for (int i = 0; i < n; ++i) triples.emplace_back(a[i], b[i], i);
sort(triples.begin(), triples.end(), [](auto &L, auto &R){
if (get<0>(L) != get<0>(R)) return get<0>(L) < get<0>(R);
return get<1>(L) < get<1>(R);
});
vector<vector<pair<int, vector<int>>>> posPairByA(n);
for (int idx = 0; idx < (int)triples.size(); ) {
int x = get<0>(triples[idx]);
int y = get<1>(triples[idx]);
vector<int> indices;
while (idx < (int)triples.size() && get<0>(triples[idx]) == x && get<1>(triples[idx]) == y) {
indices.push_back(get<2>(triples[idx]));
++idx;
}
posPairByA[x].emplace_back(y, std::move(indices));
}
vector<int> heavyY;
vector<char> isHeavy(n, 0);
for (int v = 0; v < n; ++v) {
if ((int)posA[v].size() > T) {
heavyY.push_back(v);
isHeavy[v] = 1;
}
}
ll ans = 0;
auto get_pair_vec = [&posPairByA](int x, int y) -> const vector<int>* {
const auto &vec = posPairByA[x];
auto it = std::lower_bound(vec.begin(), vec.end(), y,
[](const pair<int, vector<int>> &p, int val){ return p.first < val; });
if (it != vec.end() && it->first == y) return &it->second;
return nullptr;
};
for (int k = 0; k < n; ++k) {
int x = a[k], y = b[k];
const auto &Iy = posA[y];
if (Iy.empty()) continue;
if (isHeavy[y]) continue;
for (int t = 0; t < (int)Iy.size() && Iy[t] < k; ++t) {
int i = Iy[t];
const vector<int> *vec = get_pair_vec(x, b[i]);
if (!vec) continue;
int L = int(upper_bound(vec->begin(), vec->end(), i) - vec->begin());
int R = int(lower_bound(vec->begin(), vec->end(), k) - vec->begin());
ans += (ll)(R - L);
}
}
vector<int> cntI(n, 0);
vector<ll> P(n, 0);
vector<int> touchedCnt; touchedCnt.reserve(n);
vector<int> touchedP; touchedP.reserve(n);
for (int y : heavyY) {
touchedCnt.clear();
touchedP.clear();
for (int t = 0; t < n; ++t) {
if (b[t] == y) {
ans += P[a[t]];
}
if (cntI[b[t]] != 0) {
if (P[a[t]] == 0) touchedP.push_back(a[t]);
P[a[t]] += (ll)cntI[b[t]];
}
if (a[t] == y) {
if (cntI[b[t]] == 0) touchedCnt.push_back(b[t]);
cntI[b[t]]++;
}
}
for (int v : touchedCnt) cntI[v] = 0;
for (int v : touchedP) P[v] = 0;
}
return ans;
}
long long count_triples(std::vector<int> H) {
res = 0;
// #TH: a[k] max
for (int k = 2; k < H.size(); k ++) {
int i = k - H[k]; if (i < 0 || H[i] >= H[k]) continue; int j1 = k - H[i], j2 = i + H[i];
if (j1 < 0 || H[j1] >= H[k] || H[j1] != j1 - i) j1 = -1;
if (j2 >= k || H[j2] >= H[k] || H[j2] != k - j2) j2 = -1;
if (j1 != -1) add(i, j1, k); if (j2 != -1 && j1 != j2) add(i, j2, k);
}
// #TH: a[i] max
for (int i = 0; i + 2 < H.size(); i ++) {
int k = i + H[i]; if (k >= H.size() || H[k] >= H[i]) continue; int j1 = k - H[k], j2 = i + H[k];
if (j1 < 0 || H[j1] >= H[i] || H[j1] != j1 - i) j1 = -1;
if (j2 >= k || H[j2] >= H[i] || H[j2] != k - j2) j2 = -1;
if (j1 != -1) add(i, j1, k); if (j2 != -1 && j1 != j2) add(i, j2, k);
}
// #TH: a[j] max, j - i = a[i]
for (int i = 0; i + 2 < H.size(); i ++) {
int j = i + H[i]; if (j >= H.size() || H[j] <= H[i]) continue; int k = i + H[j];
if (k >= H.size() || H[k] >= H[j] || k - H[k] != j || k - j == H[i]) k = -1;
if (k != -1) add(i, j, k);
}
// #TH: a[j] max, j - i = a[k]
// for (int i = 0; i + 2 < H.size(); i ++) {
// for (int k = i + H[i] + 1; k < H.size(); k ++) {
// int j = i + H[k]; if (j != k - H[i] || j >= H.size()) continue;
// if (H[i] >= H[j] || H[j] <= H[k] || k - i != H[j] || j >= k) continue;
// // cout << "OKE: " << i << ' ' << j << ' ' << k << endl;
// add(i, j, k);
// }
// }
vector<int> a, b;
for (int i = 0; i < H.size(); i ++) a.push_back(H[i] + i);
for (int i = 0; i < H.size(); i ++) b.push_back(i - H[i]);
// for (int i = 0; i < a.size(); i ++)
// for (int j = i + 1; j < a.size(); j ++)
// for (int k = j + 1; k < a.size(); k ++)
// if (a[i] == b[k] && a[j] == a[k] && b[i] == b[j]) res ++;
res += countr(a, b);
return res;
}
int rand(int l, int r) {
static random_device rd;
static mt19937 gen(rd());
uniform_int_distribution<int> dist(l, r);
return dist(gen);
}
std::vector<int> construct_range(int M, int K) {
vector<int> save; ll attempt = 1e7 / M, val = -1;
while (attempt --) {
vector<int> res;
for (int i = 0; i < M; i ++) res.push_back(rand(1, sqrt(M)));
ll x = count_triples(res);
if (x > val) {val = x; save = res;}
}
return save;
// return {4,3,2,3,1,1,2,3,3,1,2,1,4,3,2,3,1,1,2,3};
}
