#include "sequence.h"
#include <bits/stdc++.h>
using namespace std;
#define pii pair<int, int>
#define pb push_back
#define ff first
#define ss second
int a[500100], b[500100];
int s1[500100], s2[500100], c[500100];
struct node{
pii x={1e9, -1e9};
node *l = nullptr, *r = nullptr;
node(){}
};
void upd(node *v, int l, int r, int pos, int x){
if(l == r){
v -> x = {min(v -> x.ff, x), max(v -> x.ss, x)};
return;
}
int mid = floor(((double)l + (double)r) / 2);
if(mid >= pos){
if(!v -> l) v->l = new node();
upd(v -> l, l, mid, pos, x);
}
else{
if(!v -> r) v->r = new node();
upd(v->r, mid+1, r, pos, x);
}
v -> x = {1e9, -1e9};
if(v -> l) v -> x = {min(v -> x.ff, v -> l -> x.ff), max(v -> x.ss, v -> l -> x.ss)};
if(v -> r) v -> x = {min(v -> x.ff, v -> r -> x.ff), max(v -> x.ss, v -> r -> x.ss)};
}
pii get(node *v, int l, int r, int L, int R){
if(r < L or R < l){
return {1e9, -1e9};
}
if(L <= l and r <= R){
return v -> x;
}
int mid=floor(((double)l + (double)r) / 2);
pii x = {1e9, -1e9};
if(v -> l){
pii k = get(v -> l, l, mid, L, R);
x = {min(x.ff, k.ff), max(x.ss, k.ss)};
}
if(v -> r){
pii k = get(v -> r, mid + 1, r, L, R);
x = {min(x.ff, k.ff), max(x.ss, k.ss)};
}
return x;
}
pii t[2000100];
int p[2001000];
void push(int v){
if(!p[v]) return;
t[v+v].ff += p[v];
t[v+v+1].ff += p[v];
t[v+v].ss += p[v];
t[v+v+1].ss += p[v];
p[v+v] += p[v];
p[v+v+1] += p[v];
p[v] = 0;
}
void updq(int v, int l, int r, int L, int R, int x){
if(r < L or R < l){
return;
}
if(L <= l and r <= R){
t[v].ff += x;
t[v].ss += x;
p[v] += x;
return;
}
int mid=(l+r)/2;
push(v);
updq(v+v, l, mid, L, R, x);
updq(v+v+1, mid+1, r, L, R, x);
t[v] = {min(t[v+v].ff, t[v+v+1].ff), max(t[v+v].ss, t[v+v+1].ss)};
}
pii getq(int v, int l, int r, int L, int R){
if(r < L or R < l){
return {1e9, -1e9};
}
if(L <= l and r <= R){
return t[v];
}
int mid=(l+r)/2;
push(v);
pii k1=getq(v+v, l, mid, L, R), k2=getq(v+v+1, mid+1, r, L, R);
return {min(k1.ff, k2.ff), max(k1.ss, k2.ss)};
}
vector<int> pos[500100];
int sequence(int n, vector<int> A) {
int ans = 0;
for(int i=1; i<=n; i++){
a[i] = A[i - 1];
pos[a[i]].pb(i);
}
for(int i=1; i<=n; i++){
b[i] = 1;
updq(1, 1, n, i, n, 1);
}
for(int x=1; x<=n; x++){
if(pos[x].size() == 0) continue;
int ls = 1;
vector<pii> q;
for(int i=0; i<pos[x].size(); i++){
updq(1, 1, n, pos[x][i], n, -b[pos[x][i]]);
b[pos[x][i]] = 0;
q.pb(getq(1, 1, n, ls, pos[x][i]));
ls = pos[x][i];
}
q.pb(getq(1, 1, n, ls, n));
vector<pair<pii, int> > zap;
for(int i=0; i<q.size(); i++){
zap.pb({{q[i].ss + i, q[i].ff-i}, i});
}
vector<pair<pii, int> > h;
for(int i=0; i<q.size(); i++){
h.pb({{q[i].ff+i, q[i].ss-i}, i});
}
sort(h.begin(), h.end());
sort(zap.begin(), zap.end());
ls = 0;
node *t = new node();
int d = n + 1;
for(int i=0; i<zap.size(); i++){
int L=zap[i].ff.ff, R=zap[i].ff.ss;
while(ls < h.size() and h[ls].ff.ff <= L){
upd(t, d - n, d + n, h[ls].ff.ss + d, h[ls].ss);
ls++;
}
pii dd = get(t, d-n, d+n, d+R, d+n);
ans = max(ans, max(zap[i].ss - dd.ff, dd.ss - zap[i].ss));
}
for(int i: pos[x]){
updq(1, 1, n, i, n, -1);
b[i] = -1;
}
}
return ans;
}
