#include <algorithm>
#include <array>
#include <cassert>
#include <chrono>
#include <iostream>
#include <random>
#include <vector>
using namespace std;
typedef vector<int> vi;
namespace brute {
vi st;
int n_;
void upd(int i, int x) {
i += n_;
while (i) st[i] += x, i /= 2;
}
int kth(int k) { // zero indexed
int i = 1;
while (i < n_)
if (st[i * 2] > k)
i = i * 2;
else
k -= st[i * 2], i = i * 2 + 1;
return i - n_;
}
int sequence(int n, vi a) {
for (int i = 0; i < n; i++) a[i]--;
vector<vi> ii(n);
for (int i = 0; i < n; i++) ii[a[i]].push_back(i);
auto qry = [&](int x, int l, int r) -> int {
return upper_bound(ii[x].begin(), ii[x].end(), r) -
lower_bound(ii[x].begin(), ii[x].end(), l);
};
n_ = 1;
while (n_ < n) n_ *= 2;
st = vi(n_ * 2, 0);
int ans = 0;
for (int l = 0; l < n; l++) {
for (int r = l; r < n; r++) {
upd(a[r], 1);
int u = kth((r - l) / 2);
int v = kth((r - l + 1) / 2);
ans = max(ans, max(qry(u, l, r), qry(v, l, r)));
}
for (int r = l; r < n; r++) upd(a[r], -1);
}
return ans;
}
} // namespace brute
const int N = 5e5, N_ = 1 << 19;
namespace D1 {
struct node {
int minL, minR, maxL, maxR, sum;
};
node operator+(node u, node v) {
return {min(u.minL, u.sum + v.minL), min(v.minR, v.sum + u.minR),
max(u.maxL, u.sum + v.maxL), max(v.maxR, v.sum + u.maxR),
u.sum + v.sum};
}
const node id = {0, 0, 0, 0, 0};
node st[N_ * 2];
int n_;
void activate(int i) {
st[i += n_] = {-1, -1, 0, 0, -1};
while (i /= 2) st[i] = st[i * 2] + st[i * 2 + 1];
}
node qry(int l, int r) {
node u = id, v = id;
for (l += n_, r += n_; l <= r; l /= 2, r /= 2) {
if (l & 1) u = u + st[l++];
if (~r & 1) v = st[r--] + v;
}
return u + v;
}
} // namespace D1
/*
testing x
a = # a_i < x
b = # a_i = x
c = # a_i > x
condition for median = x
a ≤ (a + b + c) / 2 < a + b
a * 2 <= a + b + c < (a + b) * 2
conditions:
- a ≤ b + c => c - a + b ≥ 0
- c < a + b => c - a - b < 0
fix two x's at l, r
s1 = c - a + b
s2 = c - a - b
condition: s1 ≥ 0, s2 < 0
obviously include everything in the middle
now you want to extend this range
can only increase/decrease both s1 and s2
if s1 < 0, needs 0 ≤ Δ = -s1
if s2 ≥ 0, needs 0 ≥ Δ = -s2 - 1
[min Δ] ≤ -s2 - 1 => [min Δ] + s2 + 1 ≤ 0
[max Δ] ≥ -s1 => [max Δ] + s1 ≥ 0
[min Δ] + [c - a - b] + 1 ≤ 0
[max Δ] + [c - a + b] ≥ 0
*/
const int M_ = 1 << 20, offset = N_, INF = 1e8;
int mx[M_ * 2];
vi reset;
void upd(int i, int x) {
reset.push_back(i);
i += offset;
i += M_;
while (i) mx[i] = max(mx[i], x), i /= 2;
}
int qry(int l, int r) {
l += offset;
r += offset;
int x = -INF;
for (l += M_, r += M_; l <= r; l /= 2, r /= 2) {
if (l & 1) x = max(x, mx[l++]);
if (~r & 1) x = max(x, mx[r--]);
}
return x;
}
void clr() {
for (int i : reset) {
i += offset;
i += M_;
while (i) mx[i] = -INF, i /= 2;
}
vi().swap(reset);
}
int minL[N], maxL[N], minR[N], maxR[N], sumL[N], sumR[N], ans;
void dnc(int l, int r) {
if (l < r) {
int m = (l + r) / 2;
dnc(l, m);
dnc(m + 1, r);
// cout << "--- " << l << ' ' << r << endl;
/*
[max Δ] + [c - a + b] ≥ 0 => right >= left
[min Δ] + [c - a - b] + 1 ≤ 0
*/
int sum = 0;
vector<array<int, 3>> left, right;
for (int i = m; i >= l; i--) {
if (i < m) sum += sumR[i];
int v = maxL[i] + sum + (m - i + 1);
int u = minL[i] + sum - (m - i + 1) + 1;
v *= -1;
left.push_back({v, u, (m - i + 1)});
// cout << "1) " << v << ' ' << u << ": " << m - i + 1 << '\n';
}
sum = 0;
for (int i = m + 1; i <= r; i++) {
sum += sumL[i];
// cout << "SUM = " << sum << endl;
int v = maxR[i] + sum + (i - m);
int u = minR[i] + sum - (i - m);
u *= -1;
right.push_back({v, u, i - m});
// cout << "2) " << v << ' ' << u << ": " << i - m << '\n';
}
sort(left.begin(), left.end());
sort(right.begin(), right.end());
int p = 0;
for (auto [u, v, k] : right) {
while (p < int(left.size()) && left[p][0] <= u) {
upd(left[p][1], left[p][2]);
p++;
}
ans = max(ans, k + qry(-offset, v));
}
clr();
}
}
void solve(int n, vi a) {
vector<vi> ii(n);
for (int i = 0; i < n; i++) ii[a[i]].push_back(i);
D1::n_ = 1;
while (D1::n_ < n) D1::n_ *= 2;
for (int i = 0; i < n; i++) D1::st[D1::n_ + i] = {0, 0, 1, 1, 1};
for (int i = D1::n_ - 1; i > 0; i--)
D1::st[i] = D1::st[i * 2] + D1::st[i * 2 + 1];
for (int x = 0; x < n; x++) {
if (ii[x].empty()) continue;
// cout << "\t TESTING value = " << x + 1 << endl;
int m = ii[x].size();
for (int p = 0; p < m; p++) {
D1::node u = D1::qry(p == 0 ? 0 : ii[x][p - 1] + 1, ii[x][p] - 1);
D1::node v = D1::qry(ii[x][p] + 1, p == m - 1 ? n - 1 : ii[x][p + 1] - 1);
// cout << u.sum << ' ';
sumL[p] = u.sum;
sumR[p] = v.sum;
minL[p] = u.minR;
maxL[p] = u.maxR;
minR[p] = v.minL;
maxR[p] = v.maxL;
}
// cout << '\n';
dnc(0, m - 1);
for (int i : ii[x]) {
D1::activate(i);
// cout << "TURNING " << i << " on\n";
}
}
}
int sequence(int n, vi a) {
for (int i = 0; i < M_ * 2; i++) mx[i] = -INF;
for (int i = 0; i < n; i++) a[i]--;
ans = 1; // self
solve(n, a);
// cout << endl << " REVERSING! " << endl;
// reverse(a.begin(), a.end());
for (int i = 0; i < n; i++) a[i] = n - a[i] - 1;
solve(n, a);
return ans;
}
#if 0
int main() {
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());
int n = 15;
while (1) {
vi a(n);
// for (int &x : a) cin >> x;
for (int &x : a) x = rng() % n + 1;
int u = sequence(n, a);
int v = brute::sequence(n, a);
if (u != v) {
cout << "BUG" << endl;
for (int x : a) cout << x << ' ';
cout << endl;
cout << "GOT " << u << " EXPECTED " << v << endl;
break;
}
}
}
#endif
