#include <bits/stdc++.h>
#include "gondola.h"
using namespace std;
typedef long long ll;
int valid(int n, int arr[]){
vector<int> chk(250001);
auto it = min_element(arr, arr+n);
rotate(arr, it, arr+n);
for(int i=0; i<n; i++){
if(chk[arr[i]]) return 0;
chk[arr[i]] = 1;
if(arr[i] <= n && i != arr[i]-arr[0]) return 0;
}
return 1;
}
int replacement(int n, int arr[], int ret[]){
auto it = min_element(arr, arr+n);
int minV = *it, minL = it-arr;
rotate(arr, arr+(minL - (minV%n) + 1 + n)%n, arr+n);
vector<int> idx(250001);
for(int i=0; i<n; i++){
idx[arr[i]] = i+1;
}
int tmp = *max_element(arr, arr+n);
for(int i=n+1; i<=tmp; i++){
if(idx[i]) ret[i-n-1] = idx[i];
else ret[i-n-1] = idx[tmp], idx[tmp] = i;
}
return tmp-n;
}
const ll MOD = 1000000009;
ll mpow(ll x, ll y){
if(!y) return 1;
if(y&1) return mpow(x, y-1)*x%MOD;
ll tmp = mpow(x, y/2);
return tmp*tmp%MOD;
}
int countReplacement(int n, int arr[]){
auto it = min_element(arr, arr+n);
rotate(arr, it, arr+n);
for(int i=0; i<n; i++) if(arr[i] <= n && i != arr[i]-arr[0]) return 0;
vector<int> tmpVec (arr, arr+n);
sort(tmpVec.begin(), tmpVec.end());
for(int i=1; i<n; i++) if(arr[i-1] == arr[i]) return 0;
ll ans = (tmpVec[0] > n) ? n : 1;
vector<int> vec (1, n);
for(int i=0; i<n; i++) if(arr[i] > n) vec.push_back(arr[i]);
sort(vec.begin(), vec.end());
for(int i=1; i<(int)vec.size(); i++){
ans *= mpow((int)vec.size() - 1, vec[i] - vec[i-1] - 1);
ans %= MOD;
}
return int(ans);
}
