#include "triples.h"
#include <bits/stdc++.h>
using namespace std;
#define m_p make_pair
#define all(x) (x).begin(),(x).end()
#define sz(x) ((int)(x).size())
#define fi first
#define se second
typedef long long ll;
mt19937 rnd(chrono::steady_clock::now().time_since_epoch().count());
mt19937 rnf(2106);
const int N = 200005, S = 800;
int n;
int h[N];
int aa[3], bb[3];
bool stg(int i, int j, int k)
{
assert(1 <= i && i < j && j < k && k <= n);
aa[0] = h[i];
aa[1] = h[j];
aa[2] = h[k];
bb[0] = j - i;
bb[1] = k - j;
bb[2] = k - i;
sort(aa, aa + 3);
sort(bb, bb + 3);
return (aa[0] == bb[0] && aa[1] == bb[1] && aa[2] == bb[2]);
}
vector<int> v[N], vv[N];
long long count_triples(std::vector<int> H)
{
n = sz(H);
for (int i = 1; i <= n; ++i)
h[i] = H[i - 1];
ll ans = 0;
for (int i = 1; i <= n; ++i)
{
int k = i + h[i];
if (k > n)
continue;
if (h[k] >= h[i])
continue;
int j1 = i + h[k];
if (stg(i, j1, k))
++ans;
int j2 = k - h[k];
if (j1 != j2 && stg(i, j2, k))
++ans;
}
for (int k = 1; k <= n; ++k)
{
int i = k - h[k];
if (i < 1)
continue;
if (h[i] >= h[k])
continue;
int j1 = k - h[i];
if (stg(i, j1, k))
++ans;
int j2 = i + h[i];
if (j1 != j2 && stg(i, j2, k))
++ans;
}
for (int i = 1; i <= n; ++i)
{
if (i + h[i] <= n)
v[i + h[i]].push_back(i);
}
for (int k = 1; k <= n; ++k)
{
if (k - h[k] >= 1)
vv[k - h[k]].push_back(k);
}
for (int x = 1; x <= n; ++x)
{
for (int t = 0; t < sz(v[x]); ++t)
{
int i = v[x][t];
int k = x + h[x] - h[i];
int j = x;
assert(1 <= i && i < j);
if (j < k && k <= n)
{
if (h[j] > h[i] && h[j] > h[k] && stg(i, x, k))
++ans;
}
}
if (sz(v[x]) + sz(vv[x]) < S)
{
for (int t = 0; t < sz(v[x]); ++t)
{
for (int tt = 0; tt < sz(vv[x]); ++tt)
{
int i = v[x][t];
int k = vv[x][tt];
int j = i + h[k];
assert(1 <= i && i < j && j < k && k <= n);
if (h[j] > h[i] && h[j] > h[k] && stg(i, j, k))
++ans;
}
}
}
else
{
for (int j = 1; j <= n; ++j)
{
int hi = h[j] - j + x;
if (hi % 2 != 0)
continue;
hi /= 2;
int hk = h[j] - hi;
if (hi < 1 || hk < 1)
continue;
int i = j - hk;
int k = j + hi;
if (1 <= i && k <= n && h[j] > h[k] && h[j] > h[i] && stg(i, j, k))
++ans;
}
}
}
for (int j = 1; j <= n; ++j)
{
if (h[j] % 2 == 0)
{
int i = j - h[j] / 2;
int k = j + h[j] / 2;
if (1 <= i && k <= n && h[j] > h[i] && h[j] > h[k] && stg(i, j, k))
--ans;
}
}
return ans;
}
std::vector<int> construct_range(int M, int K)
{
int n = M;
vector<int> h(n);
for (int i = 0; i < n; ++i)
{
if (i % 2 == 0)
h[i] = 1;
else
{
if ((i / 2) % 2 == 0)
h[i] = 2;
else
h[i] = 3;
}
}
//cout << count_triples(h) << "\n";
return h;
}
