#include "sequence.h"
#include <bits/stdc++.h>
#define pb push_back
#define fst first
#define snd second
#define fore(i,a,b) for(ll i=a,apio=b;i<apio;i++)
#define SZ(x) ((int)x.size())
#define ALL(x) x.begin(),x.end()
#define mset(a,v) memset((a),(v),sizeof(a))
#define imp(v) for(auto slkdh:v)cout<<slkdh<<" ";cout<<"\n"
using namespace std;
typedef int ll;
typedef pair<ll,ll> ii;
const ll INF=5e6;
struct node{
ll mxp,mnp,mxs,mns,sum;
};
node oper(node a, node b){
a.mxp=max(a.mxp,a.sum+b.mxp);
a.mnp=min(a.mnp,a.sum+b.mnp);
a.mxs=max(a.mxs+b.sum,b.mxs);
a.mns=min(a.mns+b.sum,b.mns);
a.sum+=b.sum;
return a;
}
node NEUT({-INF,INF,-INF,INF,0});
struct STcustom{
vector<node>t; ll n;
STcustom(ll n):t(2*n+5,node({0,0,0,0,0})),n(n){}
void upd(ll p, ll v){
p+=n;
t[p].mxp+=v,t[p].mnp+=v,t[p].mxs+=v,t[p].mns+=v,t[p].sum+=v;
for(;p>1;p>>=1)p^=p&1,t[p>>1]=oper(t[p],t[p^1]);
}
node query(ll l, ll r){
node izq=NEUT,der=NEUT;
for(l+=n,r+=n;l<r;l>>=1,r>>=1){
if(l&1)izq=oper(izq,t[l++]);
if(r&1)der=oper(t[--r],der);
}
return oper(izq,der);
}
};
const ll C=5e5,MAXN=2*C+5;
struct STree{
vector<ll>t; ll n;
STree(ll n):t(2*n+5,INF),n(n){}
void upd(ll p, ll v){
for(p+=n,t[p]=min(t[p],v);p>1;p>>=1)t[p>>1]=min(t[p],t[p^1]);
}
ll query(ll l, ll r){
ll res=INF;
for(l+=n,r+=n;l<r;l>>=1,r>>=1){
if(l&1)res=min(res,t[l++]);
if(r&1)res=min(res,t[--r]);
}
return res;
}
};
ll l[MAXN],r[MAXN];
bool cmp(ll i, ll j){
return ii({l[i],i})<ii({l[j],j});
}
const ll B=283;
int sequence(int N, std::vector<int> A) {
ll n=N;
vector<ll>a(n);
fore(i,0,n)a[i]=A[i]-1;
vector<ll>pos[n];
fore(i,0,n)pos[a[i]].pb(i);
STcustom st(n);
fore(i,0,n)st.upd(i,1);
ll res=1;
vector<ll>s(n);
fore(i,0,n)s[i]=1;
fore(i,0,n)if(SZ(pos[i])){
for(auto j:pos[i])st.upd(j,-1),s[j]--;
if(SZ(pos[i])<B){
fore(s,0,SZ(pos[i]))fore(e,s+1,SZ(pos[i])){
ll l=pos[i][s],r=pos[i][e];
ll dif=st.query(l,r+1).sum;
node pre=st.query(0,l+1),suf=st.query(r,n);
if(dif<=0){
if(dif+pre.mxs+suf.mxp+e-s+1>=0)res=max(res,e-s+1);
}
else {
if(dif+pre.mns+suf.mnp-(e-s+1)<=0)res=max(res,e-s+1);
}
}
}
else {
ll sum=0,rew=0;
vector<ll>rw(n+1);
vector<ll>ev{n};
l[n]=r[n]=rw[n]=0;
fore(j,0,n){
sum+=s[j],rew+=a[j]==i;
rw[j]=rew;
l[j]=sum-rew,r[j]=sum+rew;
ev.pb(j);
}
sort(ALL(ev),cmp); reverse(ALL(ev));
STree st(2*n+5+C);
for(auto i:ev){
res=max(res,rw[i]-st.query(0,r[i]+C+1));
st.upd(r[i]+C,rw[i]);
}
}
for(auto j:pos[i])st.upd(j,-1),s[j]--;
}
return res;
}
