#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define ii pair<int, int>
#define vi vector<int>
#define vii vector<ii>
#define eb emplace_back
#define all(x) x.begin(), x.end()
typedef long long ll;
const ll modu=1e9+9;
int valid(int n, int inputSeq[])
{
unordered_set<int> ch;
for (int i=0; i<n; i++){
ch.insert(inputSeq[i]);
}
if ((int)ch.size()==n){
int fi=1000000, se=1000000;
for (int i=0; i<n; i++){
if (1<=inputSeq[i] && inputSeq[i]<=n && inputSeq[i]<fi){
fi=inputSeq[i];
se=i;
}
}
if (fi==1000000){
return 1;
}else{
bool check=1;
for (int i=se, track=fi; i<se+n; i++, track++){
if (1<=inputSeq[i%n] && inputSeq[i%n]<=n){
if (inputSeq[i%n] == track){
}else{
check=0;
break;
}
}
}
if (check) return 1;
return 0;
}
}else{
return 0;
}
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
vii delta;
int cnt=0;
for (int i=0; i<n; i++){
if (1<=gondolaSeq[i] && gondolaSeq[i]<=n){
cnt++;
}
}
if (!cnt){
for (int i=0; i<n; i++){
delta.eb(ii(gondolaSeq[i], i+1)); //del, #
}
sort(all(delta));
vi ret;
int curr=n+1;
for (int i=0; i<n; i++){
while(1){
if (curr>delta[i].first) break;
ret.eb(delta[i].second);
delta[i].second=curr;
curr++;
}
}
int si=ret.size();
for (int i=0; i<si; i++){
replacementSeq[i]=ret[i];
}
return si;
}else if (cnt==n){
return 0;
}else{
//cout<<"XD\n";
int mini=1000000, pos=0;
for (int i=0; i<n; i++){
if (gondolaSeq[i]<mini){
mini=gondolaSeq[i];
pos=i;
}
}
int diff=mini-1;
pos-=diff;
pos%=n;
pos+=n;
pos%=n;
//cout<<pos<<endl;
vi ret;
for (int i=pos, track=1; i<n+pos; i++, ++track){
if (gondolaSeq[i%n]>n)
delta.eb(ii(gondolaSeq[i%n], track));
}
sort(all(delta));
//cout<<delta[0].second<<endl;
int curr=n+1, dels=delta.size();
for (int i=0; i<dels; i++){
while(1){
if (curr>delta[i].first) break;
ret.eb(delta[i].second);
delta[i].second=curr;
curr++;
}
}
int si=ret.size();
for (int i=0; i<si; i++){
replacementSeq[i]=ret[i];
}
return si;
}
}
//----------------------
ll supapower(ll b, ll ex){
if (!ex)
return 1;
if (ex&1)
return (supapower((b*b)%modu, ex/2) * b) % modu;
return supapower((b*b)%modu, ex/2) % modu;
}
int countReplacement(int n, int inputSeq[])
{
unordered_set<int> ch;
for (int i=0; i<n; i++){
ch.insert(inputSeq[i]);
}
bool alldiff=0, fcase=1;
if ((int)ch.size()==n){
int fi=1000000, se=1000000;
for (int i=0; i<n; i++){
if (1<=inputSeq[i] && inputSeq[i]<=n && inputSeq[i]<fi){
fi=inputSeq[i];
se=i;
}
}
if (fi==1000000){
alldiff=1;
}else{
//bool check=1;
for (int i=se, track=fi; i<se+n; i++, track++){
if (1<=inputSeq[i%n] && inputSeq[i%n]<=n){
if (inputSeq[i%n] == track){
}else{
fcase=0;
break;
}
}
}
}
}else{
return 0;
}
if (fcase == alldiff && !alldiff)
return 0;
ll ans=1;
vi aux;
for (int i=0; i<n; i++){
if (inputSeq[i]>n){
aux.eb(inputSeq[i]);
}
}
int ss=aux.size();
sort(all(aux));
for (int i=0; i<ss; i++){
ll di;
if (!i){
di=aux[i]-n-1;
}else{
di=aux[i] - aux[i-1] -1;
}
if (di>0){
ans*=supapower((ll)ss-i, (ll)di);
ans%=modu;
}
}
if (alldiff)
ans*=(ll)n;
ans%=modu;
return (int)ans;
}
