#include <bits/stdc++.h>
#include "gondola.h"
typedef long long ll;
using namespace std;
#define vint vector<int>
/*int ceildiv(int one, int two) {if (one % two == 0) {return one / two;}else {return one / two + 1;}} int power(int n, int pow, int m) {if (pow == 0) return 1;if (pow % 2 == 0) {ll x = power(n, pow / 2, m);return (x * x) % m;}else return (power(n, pow - 1, m) * n) % m;} int gcd(int a, int b) { if (!b)return a; return gcd(b, a % b);} int factorial(int n, int mod) {if (n > 1)return (n * factorial(n - 1, mod)) % mod; else return 1;} int lcm(int a, int b) {return (a * b) / gcd(a, b);} vector<int> read(int n) {vector<int> a; for (int i = 0; i < n; i++) { int x; cin >> x; a.pb(x);} return a;}struct prefix_sum{vint pref;void build(vint a){pref.pb(0);for(int i = 0; i < a.size(); i++){pref.pb(pref.back()+a[i]);}}int get(int l, int r){return pref[r]-pref[l-1];}};//mesanu
*/
long long power(long long n, long long pow, long long m) {if (pow == 0) return 1;if (pow % 2 == 0) {ll x = power(n, pow / 2, m);return (x * x) % m;}else return (power(n, pow - 1, m) * n) % m;}
int valid(int n, int inputSeq[])
{
set<int> s;
int dif = -1;
for(int i = 0; i < n; i++)
{
if(inputSeq[i] <= n)
{
if(dif == -1)
{
dif = (inputSeq[i]-(i+1)+n)%n;
}
if((inputSeq[i]-(i+1)+n)%n != dif)
{
return 0;
}
}
if(s.count(inputSeq[i]))
{
return 0;
}
s.insert(inputSeq[i]);
}
return 1;
}
int replacement(int n, int gondolaSeq[], int ans[])
{
vector<pair<int, int>> to_replace;
for(int i = 0; i < n; i++)
{
gondolaSeq[i]--;
}
for(int i = 0; i < n; i++)
{
if(gondolaSeq[i] < n)
{
for(int j = 1; j < n; j++)
{
if(gondolaSeq[(i+j)%n] >= n)
{
to_replace.push_back({gondolaSeq[(i+j)%n], (gondolaSeq[i]+j)%n});
}
}
break;
}
}
if(to_replace.empty() && gondolaSeq[0] >= n)
{
for(int i = 0; i < n; i++)
{
to_replace.push_back({gondolaSeq[i], i});
}
}
sort(to_replace.begin(), to_replace.end());
int count = 0;
for(auto x : to_replace)
{
while(x.second != x.first)
{
ans[count] = x.second+1;
x.second = n+count;
count++;
}
}
return count;
}
int countReplacement(int n, int inputSeq[])
{
if(!valid(n, inputSeq))
{
return 0;
}
vector<pair<int, int>> to_replace;
for(int i = 0; i < n; i++)
{
inputSeq[i]--;
}
for(int i = 0; i < n; i++)
{
if(inputSeq[i] < n)
{
for(int j = 1; j < n; j++)
{
if(inputSeq[(i+j)%n] >= n)
{
to_replace.push_back({inputSeq[(i+j)%n], (inputSeq[i]+j)%n});
}
}
break;
}
}
long long ans = 1;
if(to_replace.empty() && inputSeq[0] >= n)
{
for(int i = 0; i < n; i++)
{
to_replace.push_back({inputSeq[i], i});
}
ans = n;
}
to_replace.push_back({n, 0});
sort(to_replace.begin(), to_replace.end());
for(int i = 1; i < to_replace.size(); i++)
{
ans*=power(to_replace.size()-i, to_replace[i].first-to_replace[i-1].first, 1000000009);
ans%=1000000009;
}
return (int)ans;
}
/*
int32_t main(){
int n;
cin >> n;
int a[n];
for(int i = 0; i < n; i++)
{
cin >> a[i];
}
cout << countReplacement(n, a);
}
*/
