#include "sequence.h"
#include <bits/stdc++.h>
#pragma GCC optimize("O3,unroll-loops")
#define pb push_back
#define F first
#define S second
#define all(a) a.begin(),a.end()
#define pii pair <int,int>
#define PII pair<pii , pii>
#define ld long double
#define ll long long
#define sz(v) (int)v.size()
#define rep(i , a , b) for(int i=a;i <= b;i++)
#define per(i , a , b) for(int i=a;i >= b;i--)
using namespace std ;
const int maxn = 5e5+10 , N = 1e5 +1 , maxq = 202 , inf = 1e9 , maxk = 2022 , mod =1e9+7 ;
int a[maxn] , n;
struct node{
int mxp , mnp , mxs , mns , sm ;
node(){
mxp = mxs = -inf ;
mnp = mns = inf ;
sm =0 ;
}
};
node seg[4*maxn] ;
node mrg(node a , node b){
node r ;
r.mxp = max(a.mxp , b.mxp + a.sm) ;
r.mnp = min(a.mnp , b.mnp + a.sm) ;
r.mxs = max(b.mxs , a.mxs + b.sm);
r.mns = min(b.mns , a.mns + b.sm) ;
r.sm = a.sm + b.sm ;
return r ;
}
void upd(int x , int w, int p = 1, int l = 1 , int r = n){
if(l == r){
seg[p].mxp = seg[p].mxs = max(0 , w);
seg[p].mnp = seg[p].mns = min(0 , w) ;
seg[p].sm = w ;
return ;
}
int pl = p<<1,pr=p<<1|1 , mid = (l+r)/2 ;
if(mid>= x){
upd(x,w,pl,l,mid);
}else{
upd(x,w,pr,mid+1,r);
}
seg[p] = mrg(seg[pl] , seg[pr]) ;
}
node query(int le ,int ri ,int p = 1, int l = 1, int r= n){
int pl = p<<1,pr=p<<1|1 , mid = (l+r)/2 ;
if(le > ri){
node r ;
r.mxp = r.mxs = r.mns = r.mnp = 0 ;
return r;
}
if(le <= l && r <= ri)return seg[p] ;
if(mid >= ri){
return query(le,ri,pl,l,mid);
}
if(mid < le)return query(le,ri,pr,mid+1,r);
return mrg(query(le,ri,pl,l,mid) , query(le,ri,pr,mid+1,r)) ;
}
vector <int> vec[maxn] ;
int ch(int x){
rep(i , 0 , 4*n){
node x ;
seg[i] = x;
}
rep(i ,1 ,n){
upd(i , 1) ;
}
rep(i ,1 ,n){
if(sz(vec[i]) < x){
for(int j : vec[i]){
upd(j , -1) ;
}
continue ;
}
rep(j , 0 ,x-1){
upd(vec[i][j] , 0) ;
}
rep(j , 0 ,sz(vec[i])-x){
int l = vec[i][j] , r = vec[i][j+x-1] ;
node a1 = query(1 , l-1) , a2 =query(r+1 , n);
int sum = query(l , r).sm ;
if((sum >= 0 && sum+a1.mns+a2.mnp <= x) || (sum <= 0 && -(sum + a1.mxs + a2.mxp) <= x))return 1 ;
upd(vec[i][j] , -1) ;
if(i!=sz(vec[i])-x){
upd(vec[i][j+x] , 0) ;
}
}
rep(j , 0 ,sz(vec[i])-1){
upd(vec[i][j] , -1) ;
}
}
return 0 ;
}
int sequence(int N, vector<int> A) {
n = N ;
rep(i , 1,n){
a[i] = A[i-1] ;
vec[a[i]].pb(i) ;
}
int l = 0 , r= n+1 ;
while(r-l > 1){
int mid = (l+r)/2 ;
if(ch(mid) == 1) l = mid ;
else r = mid ;
}
return l;
}
