#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define pii pair<int, int>
#define mp make_pair
#define pb push_back
#define fi first
#define se second
const int MOD = 1000000009;
int ooga[100005];
int expo(int a, int b){
int res=1;
for (;b;b>>=1, a=(a*a)%MOD)if (b&1)res=(res*a)%MOD;
return res;
}
void init(int n, int vect[]){
int a=0;
for (int i=0; i<n; ++i)if (vect[i]<=n){
a=(vect[i]-1-i+n)%n;
break;
}
for (int i=0; i<n; ++i)ooga[(i+a)%n]=vect[i];
for (int i=0; i<n; ++i)vect[i]=ooga[i];
}
int valid(int n, int vect[]){
set<int> s;
for (int i=0; i<n; ++i)s.insert(vect[i]);
if (s.size()!=n)return 0;
init(n, vect);
for (int i=0; i<n; ++i)if (vect[i]<=n&&vect[i]-1!=i)return 0;
return 1;
}
int replacement(int n, int vect[], int ans[]){
init(n, vect);
int len=0;
vector<pii> temp;
for (int i=0; i<n; ++i)if (vect[i]>n)temp.pb(mp(vect[i], i));
sort(temp.begin(), temp.end());
for (int i=0, c=n; i<temp.size(); ++i){
++c, ans[len]=temp[i].se+1, ++len;
for (;c<temp[i].fi;++c)ans[len]=c, ++len;
}
return len;
}
int countReplacement(int n, int vect[]){
init(n, vect);
if (!valid(n, vect))return 0;
vector<int> temp;
for (int i=0; i<n; ++i)if (vect[i]>n)temp.pb(temp[i]);
sort(temp.begin(), temp.end());
int ans=(temp.size()==n?n:1);
for (int i=0, p=n+1; i<temp.size(); ++i)ans=(ans*expo(temp.size()-i, temp[i]-p))%MOD, p=temp[i]+1;
return ans;
}
