#include <bits/stdc++.h>
#include "gondola.h"
#define f first
#define s second
#define mp make_pair
#define rep replacementSeq
#define MOD 1000000009
using namespace std;
typedef long long ll;
const int MAXN = 1e6+5;
map<int,int> v;
int valid(int n, int inputSeq[])
{
for(int i=0;i<n;i++){
if(v[inputSeq[i]])return 0;
v[inputSeq[i]]=1;
}
int mini=min_element(inputSeq,inputSeq+n)-inputSeq;
int ans=1;
if(inputSeq[mini]>n)return 1;
int i=(mini-inputSeq[mini]+1+n)%n;
for(int j=0;j<n-1;j++){
if(inputSeq[(i+j)%n]>n||inputSeq[(i+j+1)%n]>n)continue;
ans*=(inputSeq[(i+j)%n]+1==inputSeq[(i+j+1)%n]);
}
return ans;
}
//----------------------
vector<pair<int,int> > a;
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int ind=-1;
for(int i=0;i<n;i++)if(gondolaSeq[i]<=n)ind=i;
if(ind==-1){
for(int j=0;j<n;j++)a.push_back(mp(gondolaSeq[j],j+1));
}else{
ind=(ind-gondolaSeq[ind]+1+n)%n;
for(int j=0;j<n;j++)a.push_back(mp(gondolaSeq[(ind+j)%n],j+1));
}
sort(a.begin(),a.end());
int id=0;
int k=n;
for(pair<int,int> x:a){
if(x.f==x.s)continue;
rep[id++]=x.s;
for(k+=1;k<x.f;k++)rep[id++]=k;
}
return id;
}
//----------------------
ll pot(int n, int a){
if(n==0)return 1;
ll h=pot(n/2,a)%MOD;
h=(h*h)%MOD;
if(n%2)h=(h*(ll)a)%MOD;
return h;
}
int countReplacement(int n, int inputSeq[])
{
if(!valid(n,inputSeq))return 0;
ll ans=1;
sort(inputSeq,inputSeq+n);
if(inputSeq[0]>n)ans=n;
int k=n;
for(int i=0;i<n;i++){
if(inputSeq[i]<=k)continue;
ans=(ans*pot(inputSeq[i]-k-1,n-i))%MOD;
k=inputSeq[i];
}
return ans%MOD;
}
