#include "gondola.h"
#include <iostream>
#include <vector>
#include <cmath>
#include <algorithm>
#include <string>
#include <map>
#include <unordered_map>
#include <set>
#include <unordered_set>
#include <queue>
#include <deque>
#include <list>
#include <iomanip>
#include <stdlib.h>
#include <time.h>
#include <cstring>
using namespace std;
typedef long long int ll;
typedef unsigned long long int ull;
typedef long double ld;
#define REP(i,a,b) for(ll i=(ll) a; i<(ll) b; i++)
#define pb push_back
#define mp make_pair
#define pl pair<ll,ll>
#define ff first
#define ss second
#define whole(x) x.begin(),x.end()
#define DEBUG(i) cout<<"Pedro Is The Master "<<i<<endl
#define INF 500000000LL
#define EPS 0.00000001
#define pi 3.14159
ll mod=1000000009LL;
template<class A=ll>
void Out(vector<A> a) {REP(i,0,a.size()) {cout<<a[i]<<" ";} cout<<endl;}
ll fastexp(ll a,ll e)
{
if(e==0) {return 1LL;}
if(e%2LL==0)
{
ll v=fastexp(a,(ll) e/2LL); return (v*v)%mod;
}
else
{
ll v=fastexp(a,(ll) e/2LL); return (((v*v)%mod)*a)%mod;
}
}
int valid(int n, int inputSeq[])
{
ll N=(ll) n;
vector<ll> s; REP(i,0,N) {s.pb((ll) inputSeq[i]);}
vector<ll> copy = s; sort(whole(copy));
REP(i,0,N-1) {if(copy[i]==copy[i+1]) {return 0;}}
REP(i,0,N) {if(s[i]>N) {s[i]=-1;} else {s[i]--;}}
ll fi=-1;
REP(i,0,N) {if(s[i]!=-1) {fi=i; break;}}
if(fi==-1) {return 1;}
REP(i,0,N)
{
if(s[i]==-1) {continue;}
if(((s[i]-i)-(s[fi]-fi))%N!=0) {return 0;}
}
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int r[])
{
ll N =(ll) n; vector<ll> s; REP(i,0,N) {s.pb((ll) gondolaSeq[i]);}
REP(i,0,N)
{
if(s[i]<=N)
{
ll shift = (s[i]-1LL-i)%N; //shift to the right
vector<ll> copy_s; REP(j,0,N) {copy_s.pb(s[(j-shift+N)%N]);}
s=copy_s; break;
}
}
ll max_ind = (ll) (max_element(whole(s))-s.begin());
ll R = s[max_ind]-N;
unordered_map<ll,ll> m;
REP(i,0,N) {m[s[i]]=i;}
ll last = max_ind+1;
REP(i,0,R)
{
ll val = N+i+1;
unordered_map<ll,ll>::iterator it = m.find(val);
if(it==m.end()) {r[i]=last; last=val;}
else if(m[val]!=max_ind) {r[i]=m[val]+1;}
else {r[i]=last; last=val;}
}
return R;
}
//----------------------
int countReplacement(int n, int inputSeq[])
{
if(!valid(n,inputSeq)) {return 0;}
ll N =(ll) n; vector<ll> s; REP(i,0,N) {s.pb((ll) inputSeq[i]);}
vector<ll> p;
REP(i,0,N) {if(s[i]<=N) {continue;} p.pb(s[i]-N);}
sort(whole(p));
REP(i,0,p.size()) {p[i]-=(i+1);}
ll ans=1LL;
ll last=0LL;
REP(i,0,p.size())
{
ll val = fastexp(p.size()-i,p[i]-last); ans*=val; ans%=mod;
last=p[i];
}
if(*min_element(whole(s))>N) {ans*=N;}
ans+=mod; ans%=mod;
return ans;
}
