#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int MOD = 1e9 + 9;
int valid(int n, int arr[]){
set<int> s;
set<int> s2;
int cnt = 0;
for(int i = 0; i < n; i++){
if(arr[i] <= n) s.insert((arr[i] - i + n) % n);
else cnt++;
s2.insert(arr[i]);
}
if(!(s2.size() == n && s.size() == 1)) return 0;
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
return -2;
}
//----------------------
ll binpow(ll a, ll b){
ll res = 1;
while(b){
if(b & 1) res = res * a % MOD;
b /= 2;
a = a * a % MOD;
}
return res;
}
int countReplacement(int n, int arr[]){
set<int> s;
set<int> s2;
vector<int> v;
for(int i = 0; i < n; i++){
if(arr[i] <= n) s.insert((arr[i] - i + n) % n);
else v.push_back(arr[i]);
s2.insert(arr[i]);
}
if(!(s2.size() == n && s.size() == 1)) return 0;
sort(v.begin(), v.end());
v.insert(v.begin(), n);
ll ans = 1;
for(int i = 1; i < v.size(); i++){
ans = ans * binpow(v.size() - i, v[i] - v[i - 1] - 1) % MOD;
}
if(v.size() == n + 1) ans = ans * n % MOD;
return ans;
}
