#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define sz(x) (int)(x.size())
const int MOD =(int)(1e9+9);
typedef long long ll;
int val[100005],p[250005];
set<int> here;
int valid(int n, int inputSeq[])
{
int idx=-1;
for (int i = 0; i < n; ++i){
if(here.find(inputSeq[i])!=here.end())return 0;
here.insert(inputSeq[i]);
if(inputSeq[i]<=n)idx=i;
}
if(idx==-1)return 1;
int h=inputSeq[idx];
for (int i = 0; i < n; ++i)
val[(idx+i)%n]=((h-1+i)%n)+1;
for (int i = 0; i < n; ++i)
if(inputSeq[i]<=n && inputSeq[i]!=val[i])return 0;
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int flag=-1;
for (int i = 0; i < n; ++i)
if(gondolaSeq[i]<=n)flag=i;
priority_queue<int,vector<int>,greater<int> > pq;
if(flag!=-1){
int g=gondolaSeq[flag];
for (int i = 0; i < n; ++i){
int r=((g-1+i)%n)+1;
if(gondolaSeq[(flag+i)%n]!=r)pq.push(gondolaSeq[(flag+i)%n]),p[gondolaSeq[(flag+i)%n]]=r;
}
}
else{
for (int i = 0; i < n; ++i)
p[gondolaSeq[i]]=i+1,pq.push(gondolaSeq[i]);
}
int h=n+1,idx=0;
while(!pq.empty()){
int f=pq.top();
pq.pop();
replacementSeq[idx++]=p[f];
while(h<f)replacementSeq[idx++]=h++;
h++;
}
return idx;
}
//----------------------
int binpow(int a,int b){
if(!b)return 1;
ll h=binpow(a,b>>1);
h*=h;
if(h>=MOD)h%=MOD;
if(b&1)h*=a;
if(h>=MOD)h%=MOD;
return (int)(h);
}
int countReplacement(int n, int inputSeq[])
{
if(!valid(n,inputSeq))return 0;
vector<int> vec={n};
bool flag=0;
for (int i = 0; i < n; ++i){
if(inputSeq[i]>n)
vec.push_back(inputSeq[i]);
else flag=1;
}
ll ans=1;
sort(vec.begin(),vec.end());
for (int i = 1; i < sz(vec); ++i)
ans=(ans*(ll)binpow(sz(vec)-i,vec[i]-vec[i-1]-1))%MOD;
return (ans*((!flag)?n:1))%MOD;
}
