#define _CRT_SECURE_NO_WARNINGS
#include <iostream>
#include <iomanip>
#include <array>
#include <string>
#include <algorithm>
#include <cmath>
#include <set>
#include <map>
#include <unordered_set>
#include <unordered_map>
#include <vector>
#include <stack>
#include <queue>
#include <deque>
#include <bitset>
#include <list>
#include <iterator>
#include <numeric>
#include <complex>
#include <utility>
#include <random>
#include <cassert>
#include <fstream>
#include "sequence.h"
using namespace std;
mt19937 rnd(7069);
typedef int itn;
typedef long long ll;
typedef unsigned long long ull;
typedef double db;
typedef float fl;
typedef long double ld;
using vi = vector<int>;
using vll = vector<ll>;
using mii = map<int, int>;
using mll = map<ll, ll>;
using pii = pair<int, int>;
using pll = pair<ll, ll>;
#define ff first
#define ss second
#define pub push_back
#define pob pop_back
#define puf push_front
#define pof pop_front
#define mpr make_pair
#define yes cout<<"Yes\n"
#define no cout<<"No\n"
#define all(x) (x).begin(), (x).end()
const int MAX = int(2e9 + 5);
const ll MAXL = ll(1e18) + 5ll;
const int N = 500005;
int a[N], f[N], pref[N], suf[N], lazy_pref[N * 4], lazy_suf[N * 4], ran[N * 4];
pii id[N], t_pref[N * 4], t_suf[N * 4];
int n;
void add_fen(int ind, int val) {
while (ind <= n) {
f[ind] += val;
ind += (ind & -ind);
}
}
int sum_fen(int ind) {
int ret = 0;
while (ind) {
ret += f[ind];
ind -= (ind & -ind);
}
return ret;
}
int qry_fen(int l, int r) {
return sum_fen(r) - sum_fen(l - 1);
}
void prop(int pos) {
t_pref[2 * pos].ff += lazy_pref[pos] * ran[2 * pos];
t_pref[2 * pos + 1].ff += lazy_pref[pos] * ran[2 * pos + 1];
t_pref[2 * pos].ss += lazy_pref[pos] * ran[2 * pos];
t_pref[2 * pos + 1].ss += lazy_pref[pos] * ran[2 * pos + 1];
lazy_pref[2 * pos] += lazy_pref[pos];
lazy_pref[2 * pos + 1] += lazy_pref[pos];
lazy_pref[pos] = 0;
t_suf[2 * pos].ff += lazy_suf[pos] * ran[2 * pos];
t_suf[2 * pos + 1].ff += lazy_suf[pos] * ran[2 * pos + 1];
t_suf[2 * pos].ss += lazy_suf[pos] * ran[2 * pos];
t_suf[2 * pos + 1].ss += lazy_suf[pos] * ran[2 * pos + 1];
lazy_suf[2 * pos] += lazy_suf[pos];
lazy_suf[2 * pos + 1] += lazy_suf[pos];
lazy_suf[pos] = 0;
}
void bld(int l = 1, int r = n, int pos = 1) {
ran[pos] = r - l + 1;
if (l == r) {
t_pref[pos].ff = t_pref[pos].ss = pref[l];
t_suf[pos].ff = t_suf[pos].ss = suf[l];
return;
}
int mid = (l + r) / 2;
bld(l, mid, 2 * pos);
bld(mid + 1, r, 2 * pos + 1);
t_pref[pos].ff = min(t_pref[2 * pos].ff, t_pref[2 * pos + 1].ff);
t_pref[pos].ss = max(t_pref[2 * pos].ss, t_pref[2 * pos + 1].ss);
t_suf[pos].ff = min(t_suf[2 * pos].ff, t_suf[2 * pos + 1].ff);
t_suf[pos].ss = max(t_suf[2 * pos].ss, t_suf[2 * pos + 1].ss);
}
int qry_min(int l, int r, int type, int tl = 1, int tr = n, int pos = 1) {
if (l == tl && r == tr) {
return (type == 1 ? t_pref[pos].ff : t_suf[pos].ff);
}
prop(pos);
int mid = (tl + tr) / 2;
if (mid >= r) {
return qry_min(l, r, type, tl, mid, 2 * pos);
}
if (mid < l) {
return qry_min(l, r, type, mid + 1, tr, 2 * pos + 1);
}
return min(qry_min(l, mid, type, tl, mid, 2 * pos), qry_min(mid + 1, r, type, mid + 1, tr, 2 * pos + 1));
}
int qry_max(int l, int r, int type, int tl = 1, int tr = n, int pos = 1) {
if (l == tl && r == tr) {
return (type == 1 ? t_pref[pos].ss : t_suf[pos].ss);
}
prop(pos);
int mid = (tl + tr) / 2;
if (mid >= r) {
return qry_max(l, r, type, tl, mid, 2 * pos);
}
if (mid < l) {
return qry_max(l, r, type, mid + 1, tr, 2 * pos + 1);
}
return max(qry_max(l, mid, type, tl, mid, 2 * pos), qry_max(mid + 1, r, type, mid + 1, tr, 2 * pos + 1));
}
void add(int l, int r, int val, int type, int tl = 1, int tr = n, int pos = 1) {
if (l == tl && r == tr) {
if (type == 1) {
t_pref[pos].ff += val * ran[pos];
t_pref[pos].ss += val * ran[pos];
lazy_pref[pos] += val;
}
else {
t_suf[pos].ff += val * ran[pos];
t_suf[pos].ss += val * ran[pos];
lazy_suf[pos] += val;
}
return;
}
prop(pos);
int mid = (tl + tr) / 2;
if (mid >= r) {
add(l, r, val, type, tl, mid, 2 * pos);
}
else if (mid < l) {
add(l, r, val, type, mid + 1, tr, 2 * pos + 1);
}
else {
add(l, mid, val, type, tl, mid, 2 * pos);
add(mid + 1, r, val, type, mid + 1, tr, 2 * pos + 1);
}
t_pref[pos].ff = min(t_pref[2 * pos].ff, t_pref[2 * pos + 1].ff);
t_pref[pos].ss = max(t_pref[2 * pos].ss, t_pref[2 * pos + 1].ss);
t_suf[pos].ff = min(t_suf[2 * pos].ff, t_suf[2 * pos + 1].ff);
t_suf[pos].ss = max(t_suf[2 * pos].ss, t_suf[2 * pos + 1].ss);
}
int sequence(int N, std::vector<int> A) {
n = N;
int ans = 1;
for (int i = 1; i <= n; ++i) {
a[i] = A[i - 1];
if (a[i] != 1) {
add_fen(i, 1);
pref[i] = suf[i] = 1;
}
pref[i] += pref[i - 1];
if (!id[a[i]].ff) id[a[i]].ff = i;
id[a[i]].ss = i;
}
for (int i = n; i >= 1; --i) {
suf[i] += suf[i + 1];
}
bld();
int l, r;
for (int i = 1; i <= n; ++i) {
l = id[i].ff, r = id[i].ss;
if (i != 1 && l) {
add_fen(l, -1);
if (l != r) add_fen(r, -1);
add(l, n, -1, 1);
add(1, l, -1, 2);
if (l != r) {
add(r, n, -1, 1);
add(1, r, -1, 2);
}
}
if (r && l != r) {
int g = qry_fen(l, r);
if (g >= -2 && g <= 2) {
ans = 2;
break;
}
if (g < -2) {
int mx1 = qry_max(1, l, 2) - qry_max(l, l, 2);
int mx2 = qry_max(r, n, 1) - qry_max(r, r, 1);
if (mx1 + mx2 + g >= -2) {
ans = 2;
break;
}
}
if (g > 2) {
int mn1 = qry_min(1, l, 2) - qry_min(l, l, 2);
int mn2 = qry_min(r, n, 1) - qry_min(r, r, 1);
if (mn1 + mn2 + g <= 2) {
ans = 2;
break;
}
}
}
if (l) {
add_fen(l, -1);
if (l != r) add_fen(r, -1);
add(l, n, -1, 1);
add(1, l, -1, 2);
if (l != r) {
add(r, n, -1, 1);
add(1, r, -1, 2);
}
}
}
return ans;
}
/*
6
1 2 3 1 2 3
3
9
1 1 2 3 4 3 2 1 1
2
14
2 6 2 5 3 4 2 1 4 3 5 6 3 2
3
*/
