#include "sequence.h"
#include <bits/stdc++.h>
#define SZ(s) ((int) ((s).size()))
using namespace std;
bool is_sub_3(const std::vector<int> a) {
auto mit = max_element(a.begin(), a.end());
return std::is_sorted(a.begin(), mit)
&& std::is_sorted(mit, a.end(), std::greater<int>());
}
int len(const std::pair<int,int>& p) {
return p.second - p.first + 1;
}
bool can_be_median(int cnt_less, int cnt_equal, int cnt_greater) {
return cnt_equal + cnt_less >= cnt_greater;
}
int sub3(const vector<int>& a) {
int n = SZ(a);
unordered_map<int, vector<pair<int,int>>> pos;
int l = 0;
while (l < n) {
int r = l;
while (r < n && a[l] == a[r]) ++r;
pos[a[l]].emplace_back(l, r-1);
l = r;
}
int res = 0;
for (const auto& [val, lrs] : pos) {
// only 1 segment
for (const auto& lr : lrs) res = max(res, len(lr));
// 2 segments
if (SZ(lrs) < 2) continue;
assert(SZ(lrs) == 2);
int cnt_equal = len(lrs[0]) + len(lrs[1]);
int cnt_greater = len({lrs[0].second + 1, lrs[1].first - 1});
int cnt_less = len({0, lrs[0].first - 1}) + len({lrs[1].second + 1, n-1});
if (can_be_median(cnt_less, cnt_equal, cnt_greater)) {
res = max(res, cnt_equal);
}
}
return res;
}
// SegTree, copied from AtCoder library {{{
// AtCoder doc: https://atcoder.github.io/ac-library/master/document_en/segtree.html
//
// Notes:
// - Index of elements from 0 -> n-1
// - Range queries are [l, r-1]
//
// Tested:
// - (binary search) https://atcoder.jp/contests/practice2/tasks/practice2_j
// - https://oj.vnoi.info/problem/gss
// - https://oj.vnoi.info/problem/nklineup
// - (max_right & min_left for delete position queries) https://oj.vnoi.info/problem/segtree_itstr
// - https://judge.yosupo.jp/problem/point_add_range_sum
// - https://judge.yosupo.jp/problem/point_set_range_composite
int ceil_pow2(int n) {
int x = 0;
while ((1U << x) < (unsigned int)(n)) x++;
return x;
}
template<
class T, // data type for nodes
T (*op) (T, T), // operator to combine 2 nodes
T (*e)() // identity element
>
struct SegTree {
SegTree() : SegTree(0) {}
explicit SegTree(int n) : SegTree(vector<T> (n, e())) {}
explicit SegTree(const vector<T>& v) : _n((int) v.size()) {
log = ceil_pow2(_n);
size = 1<<log;
d = vector<T> (2*size, e());
for (int i = 0; i < _n; i++) d[size+i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
// 0 <= p < n
void set(int p, T x) {
assert(0 <= p && p < _n);
p += size;
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
// 0 <= p < n
T get(int p) const {
assert(0 <= p && p < _n);
return d[p + size];
}
// Get product in range [l, r-1]
// 0 <= l <= r <= n
// For empty segment (l == r) -> return e()
T prod(int l, int r) const {
assert(0 <= l && l <= r && r <= _n);
T sml = e(), smr = e();
l += size;
r += size;
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
T all_prod() const {
return d[1];
}
// Binary search on SegTree to find largest r:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l] .. a[r])) = false (assuming op(..., a[n]), which is out of bound, is always false)
template <bool (*f)(T)> int max_right(int l) const {
return max_right(l, [](T x) { return f(x); });
}
template <class F> int max_right(int l, F f) const {
assert(0 <= l && l <= _n);
assert(f(e()));
if (l == _n) return _n;
l += size;
T sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!f(op(sm, d[l]))) {
while (l < size) {
l = (2 * l);
if (f(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
// Binary search on SegTree to find smallest l:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l-1] .. a[r-1])) = false (assuming op(a[-1], ..), which is out of bound, is always false)
template <bool (*f)(T)> int min_left(int r) const {
return min_left(r, [](T x) { return f(x); });
}
template <class F> int min_left(int r, F f) const {
assert(0 <= r && r <= _n);
assert(f(e()));
if (r == 0) return 0;
r += size;
T sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!f(op(d[r], sm))) {
while (r < size) {
r = (2 * r + 1);
if (f(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
vector<T> d;
void update(int k) {
d[k] = op(d[2*k], d[2*k+1]);
}
};
// }}}
// SegTree examples {{{
// Examples: Commonly used SegTree ops: max / min / sum
struct MaxSegTreeOp {
static int op(int x, int y) {
return max(x, y);
}
static int e() {
return INT_MIN;
}
};
struct MinSegTreeOp {
static int op(int x, int y) {
return min(x, y);
}
static int e() {
return INT_MAX;
}
};
struct SumSegTreeOp {
static long long op(long long x, long long y) {
return x + y;
}
static long long e() {
return 0;
}
};
// using STMax = SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e>;
// using STMin = SegTree<int, MinSegTreeOp::op, MinSegTreeOp::e>;
// using STSum = SegTree<int, SumSegTreeOp::op, SumSegTreeOp::e>;
// }}}
// Lazy Segment Tree, copied from AtCoder {{{
// Source: https://github.com/atcoder/ac-library/blob/master/atcoder/lazysegtree.hpp
// Doc: https://atcoder.github.io/ac-library/master/document_en/lazysegtree.html
//
// Notes:
// - Index of elements from 0
// - Range queries are [l, r-1]
// - composition(f, g) should return f(g())
//
// Tested:
// - https://oj.vnoi.info/problem/qmax2
// - https://oj.vnoi.info/problem/lites
// - (range set, add, mult, sum) https://oj.vnoi.info/problem/segtree_itmix
// - (range add (i-L)*A + B, sum) https://oj.vnoi.info/problem/segtree_itladder
// - https://atcoder.jp/contests/practice2/tasks/practice2_l
// - https://judge.yosupo.jp/problem/range_affine_range_sum
template<
class S, // node data type
S (*op) (S, S), // combine 2 nodes
S (*e) (), // identity element
class F, // lazy propagation tag
S (*mapping) (F, S), // apply tag F on a node
F (*composition) (F, F), // combine 2 tags
F (*id)() // identity tag
>
struct LazySegTree {
LazySegTree() : LazySegTree(0) {}
explicit LazySegTree(int n) : LazySegTree(vector<S>(n, e())) {}
explicit LazySegTree(const vector<S>& v) : _n((int) v.size()) {
log = ceil_pow2(_n);
size = 1 << log;
d = std::vector<S>(2 * size, e());
lz = std::vector<F>(size, id());
for (int i = 0; i < _n; i++) d[size + i] = v[i];
for (int i = size - 1; i >= 1; i--) {
update(i);
}
}
// 0 <= p < n
void set(int p, S x) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = x;
for (int i = 1; i <= log; i++) update(p >> i);
}
// 0 <= p < n
S get(int p) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
return d[p];
}
// Get product in range [l, r-1]
// 0 <= l <= r <= n
// For empty segment (l == r) -> return e()
S prod(int l, int r) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return e();
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
S sml = e(), smr = e();
while (l < r) {
if (l & 1) sml = op(sml, d[l++]);
if (r & 1) smr = op(d[--r], smr);
l >>= 1;
r >>= 1;
}
return op(sml, smr);
}
S all_prod() {
return d[1];
}
// 0 <= p < n
void apply(int p, F f) {
assert(0 <= p && p < _n);
p += size;
for (int i = log; i >= 1; i--) push(p >> i);
d[p] = mapping(f, d[p]);
for (int i = 1; i <= log; i++) update(p >> i);
}
// Apply f on all elements in range [l, r-1]
// 0 <= l <= r <= n
void apply(int l, int r, F f) {
assert(0 <= l && l <= r && r <= _n);
if (l == r) return;
l += size;
r += size;
for (int i = log; i >= 1; i--) {
if (((l >> i) << i) != l) push(l >> i);
if (((r >> i) << i) != r) push((r - 1) >> i);
}
{
int l2 = l, r2 = r;
while (l < r) {
if (l & 1) all_apply(l++, f);
if (r & 1) all_apply(--r, f);
l >>= 1;
r >>= 1;
}
l = l2;
r = r2;
}
for (int i = 1; i <= log; i++) {
if (((l >> i) << i) != l) update(l >> i);
if (((r >> i) << i) != r) update((r - 1) >> i);
}
}
// Binary search on SegTree to find largest r:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l] .. a[r])) = false (assuming op(..., a[n]), which is out of bound, is always false)
template <bool (*g)(S)> int max_right(int l) {
return max_right(l, [](S x) { return g(x); });
}
template <class G> int max_right(int l, G g) {
assert(0 <= l && l <= _n);
assert(g(e()));
if (l == _n) return _n;
l += size;
for (int i = log; i >= 1; i--) push(l >> i);
S sm = e();
do {
while (l % 2 == 0) l >>= 1;
if (!g(op(sm, d[l]))) {
while (l < size) {
push(l);
l = (2 * l);
if (g(op(sm, d[l]))) {
sm = op(sm, d[l]);
l++;
}
}
return l - size;
}
sm = op(sm, d[l]);
l++;
} while ((l & -l) != l);
return _n;
}
// Binary search on SegTree to find smallest l:
// f(op(a[l] .. a[r-1])) = true (assuming empty array is always true)
// f(op(a[l-1] .. a[r-1])) = false (assuming op(a[-1], ..), which is out of bound, is always false)
template <bool (*g)(S)> int min_left(int r) {
return min_left(r, [](S x) { return g(x); });
}
template <class G> int min_left(int r, G g) {
assert(0 <= r && r <= _n);
assert(g(e()));
if (r == 0) return 0;
r += size;
for (int i = log; i >= 1; i--) push((r - 1) >> i);
S sm = e();
do {
r--;
while (r > 1 && (r % 2)) r >>= 1;
if (!g(op(d[r], sm))) {
while (r < size) {
push(r);
r = (2 * r + 1);
if (g(op(d[r], sm))) {
sm = op(d[r], sm);
r--;
}
}
return r + 1 - size;
}
sm = op(d[r], sm);
} while ((r & -r) != r);
return 0;
}
private:
int _n, size, log;
vector<S> d;
vector<F> lz;
void update(int k) {
d[k] = op(d[2*k], d[2*k+1]);
}
void all_apply(int k, F f) {
d[k] = mapping(f, d[k]);
if (k < size) lz[k] = composition(f, lz[k]);
}
void push(int k) {
all_apply(2*k, lz[k]);
all_apply(2*k+1, lz[k]);
lz[k] = id();
}
};
// }}}
int sub4(int n, const std::vector<int>& a) {
int res = 0;
int ln = *max_element(a.begin(), a.end());
for (int median = 0; median <= ln; ++median) {
vector<int> cnt_less(n, 0);
vector<int> cnt_equal(n, 0);
vector<int> cnt_greater(n, 0);
for (int i = 0; i < n; ++i) {
cnt_less[i] = a[i] < median;
cnt_equal[i] = a[i] == median;
cnt_greater[i] = a[i] > median;
}
std::partial_sum(cnt_less.begin(), cnt_less.end(), cnt_less.begin());
std::partial_sum(cnt_equal.begin(), cnt_equal.end(), cnt_equal.begin());
std::partial_sum(cnt_greater.begin(), cnt_greater.end(), cnt_greater.begin());
// cnt_less[r] + cnt_equal[r] - cnt_greater[r]
// >= cnt_less[l-1] + cnt_equal[l-1] - cnt_greater[l-1]
//
// cnt_less[r] - cnt_equal[r] - cnt_greater[r]
// < cnt_less[l-1] - cnt_equal[l-1] - cnt_greater[l-1]
//
// l < r
vector<vector<pair<int,int>>> f1_at(n*2 + 1);
for (int i = n-1; i >= 0; --i) {
// add n so that everything >= 0
int f1 = cnt_less[i] + cnt_equal[i] - cnt_greater[i] + n;
int f2 = cnt_less[i] - cnt_equal[i] - cnt_greater[i] + n;
f1_at[f1].emplace_back(i, f2);
}
f1_at[n].emplace_back(-1, n);
SegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e> st(2*n + 1);
for (int f1 = 2*n; f1 >= 0; --f1) {
// f1(r) >= f1(l-1) && f2(r) < f2(l-1)
for (const auto& [i, f2] : f1_at[f1]) {
// l = i + 1
int max_r = st.prod(0, f2 + 1);
if (max_r > i) {
res = max(res, cnt_equal[max_r] - (i >= 0 ? cnt_equal[i] : 0));
}
// r = i
st.set(f2, max(st.get(f2), i));
}
}
}
return res;
}
using F = int;
int mapping(F f, int s) {
return f + s;
}
F composition(F f, F g) {
return f + g;
}
F id() { return 0; }
bool can(int n, int eq, const vector<int>& a, const vector<vector<int>>& ids) {
int ln = *max_element(a.begin(), a.end());
LazySegTree<int, MaxSegTreeOp::op, MaxSegTreeOp::e, F, mapping, composition, id> st_max(n + 1);
LazySegTree<int, MinSegTreeOp::op, MinSegTreeOp::e, F, mapping, composition, id> st_min(n + 1);
st_max.set(0, 0);
st_min.set(0, 0);
for (int median = 0; median <= ln; median++) {
if (median == 0) {
for (int i = 1; i <= n; ++i) {
st_max.set(i, i);
st_min.set(i, i);
}
} else {
// greater is affected?
for (int i : ids[median]) {
// previously: greater = 1, now: greater = 0
st_max.apply(i, n+1, -1);
st_min.apply(i, n+1, -1);
}
// less is affected?
for (int i : ids[median-1]) {
// previously: less = 0, now: less = 1
st_max.apply(i, n+1, -1);
st_min.apply(i, n+1, -1);
}
}
if (SZ(ids[median]) < eq) continue;
for (int ix = 0, iy = eq-1; iy < SZ(ids[median]); ++ix, ++iy) {
int x = ids[median][ix];
int y = ids[median][iy];
// find [l, r]:
// - l <= x < y <= r
// - less + eq >= greater
// - greater + eq >= less
// - eq >= greater - less >= -eq
// - eq >= (greater(r) - less(r)) - (greater(l-1) - less(l-1)) >= -eq
int max_val = st_max.prod(y, n+1) - st_min.prod(0, x);
int min_val = st_min.prod(y, n+1) - st_max.prod(0, x);
// [-eq, eq] and [min_val, max_val] intersects
if (min_val <= eq && max_val >= -eq) return true;
}
}
return false;
}
int sub5(int n, std::vector<int> a) {
// ids from 1
a.insert(a.begin(), 0);
vector<vector<int>> ids(n + 1);
for (int i = 1; i <= n; ++i) {
ids[a[i]].push_back(i);
}
int max_freq = 0;
for (int i = 1; i <= n; ++i) {
max_freq = max(max_freq, SZ(ids[i]));
}
int left = 1, right = max_freq, res = 1;
while (left <= right) {
int mid = (left + right) / 2;
if (can(n, mid, a, ids)) {
res = mid;
left = mid + 1;
} else {
right = mid - 1;
}
}
return res;
}
int sequence(int n, std::vector<int> a) {
if (is_sub_3(a)) return sub3(a);
return sub4(n, a);
}
