#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
int valid(int n, int arr[])
{
vector <int> v;
long long mn=1e18,idx=0;
for(int i=0;i<n;i++){
v.push_back(arr[i]);
if(arr[i]<mn){
mn=arr[i];
idx=i;
}
}
int cnt=1;
for(int i=idx;i<idx+n;i++){
if(arr[i%n]>n) {
arr[i%n]=cnt++;
}
if(arr[i%n]!=cnt) return 0;
cnt++;
}
sort(v.begin(),v.end());
for(int i=0;i<v.size()-1;i++) if(v[i]==v[i+1]) return 0;
return 1;
}
//----------------------
int replacement(int n, int arr[], int rep[])
{
vector <int> v;
long long idx=0;
long long mx=0,idx2=0;
for(int i=0;i<n;i++){
if(arr[i]<n){
idx=(i-arr[i]+1+n)%n;
}
if(arr[i]>mx){
mx=arr[i];
idx2=i;
}
}
for(int i=0;i<mx-n;i++) rep[i]=-1;
int cnt=1;
for(int i=idx;i<idx+n;i++){
if(arr[i%n]!=cnt){
rep[arr[i%n]-n-1]=i%n;
}
arr[i%n]=cnt;
cnt++;
}
for(int i=0;i<mx-n;i++) if(rep[i]==-1) rep[i]=idx2;
int num=n+1;
for(int i=0;i<mx-n;i++){
//cout<<rep[i]<<" ";
int x=arr[rep[i]];
arr[rep[i]]=num;
rep[i]=x;
num++;
}
//cout<<endl;
return mx-n;
}
//----------------------
#define mod 1000000009
int vis[1000001];
int countReplacement(int n, int arr[])
{
if(valid(n,arr)==0) return 0;
int mx=0;
for(int i=0;i<n;i++) mx=max(arr[i],mx);
long long cnt=0,ans=1;
for(int i=0;i<n;i++){
if(arr[i]>n){
vis[arr[i]]=1;
cnt++;
}
}
for(int i=n+1;i<=mx;i++){
if(vis[i]==0){
ans*=cnt;
ans%=mod;
}
else cnt--;
}
return ans;
}
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