#include<bits/stdc++.h>
#include "gondola.h"
#define MAXN 500007
using namespace std;
const long long mod=1e9+9;
int n,pos;
int s[MAXN],last,maxs,where[MAXN],val[MAXN];
bool li[MAXN],dali;
long long ways;
int valid(int N, int inputSeq[]){
n=N;
int mins=1;
for(int i=1;i<=n;i++){
s[i]=inputSeq[i-1];
s[i+n]=s[i];
if(s[i]<s[mins]){
mins=i;
}
}
for(int i=mins;i<mins+n;i++){
if(s[i]<=n and s[i]!=s[mins]+i-mins)return 0;
if(s[i]>n){
if(li[s[i]])return 0;
li[s[i]]=true;
}
}
return 1;
}
int replacement(int N, int gondolaSeq[], int replacementSeq[]){
n=N;
maxs=1;
for(int i=1;i<=n;i++){
s[i]=gondolaSeq[i-1];
if(s[i]>s[maxs])maxs=i;
if(s[i]<=n)pos=i;
where[s[i]]=i;
}
if(pos==0){
for(int i=1;i<=n;i++)val[i]=i;
}else{
for(int i=pos;i<=n;i++)val[i]=s[pos]+i-pos;
for(int i=1;i<pos;i++)val[i]=val[n]+i;
for(int i=1;i<=n;i++){
if(val[i]>n)val[i]-=n;
}
}
for(int i=n+1;i<=s[maxs];i++){
if(where[i]==0){
replacementSeq[i-n-1]=val[maxs];
val[maxs]=i;
}else{
replacementSeq[i-n-1]=val[where[i]];
val[where[i]]=i;
}
}
return s[maxs]-n;
}
long long power(long long a,int b){
if(b==0)return 1;
if(b==1)return a;
if(b==2)return (a*a)%mod;
if(b%2==0)return power(power(a,b/2),2);
return (power(power(a,b/2),2)*a)%mod;
}
int countReplacement(int N, int inputSeq[]){
n=N;
for(int i=1;i<=n;i++){
s[i]=inputSeq[i-1];
}
sort(s+1,s+n+1);
ways=1; last=n;
for(int i=1;i<=n;i++){
if(s[i]<=n){
dali=true; continue;
}
if(!dali and last==n){
ways*=power(n-i+1,s[i]-last);
}else{
ways*=power(n-i+1,s[i]-last-1);
}
ways%=mod;
last=s[i];
}
return ways;
}
