#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
typedef int INT;
#define mp make_pair
#define pb push_back
#define fst first
#define snd second
#define int long long
#define MMAX 16384
#define fast_io() ios::sync_with_stdio(false)
#define FOR(i, l, r) for(int i = (l); i < (r); i++)
typedef long long ll;
typedef pair<ll, ll> ii;
typedef vector<int> vi;
typedef vector<ii> vii;
typedef vector<vi> vvi;
typedef set<int> si;
typedef double ld;
typedef pair<ld, ld> dd;
const ll INF = 1000000000000000000LL;
const int NMAX = 1e5+4;
const int mod = 1e9+9;
const ld eps = 1e-10;
const ld PI = acos(-1);
INT valid(INT n, INT inputSeq[]){
int k = -1;
FOR(i, 0, n) if(inputSeq[i] <= n) {k = i; break;}
if(k == -1) {
vi tmp;
FOR(i, 0, n) tmp.pb(inputSeq[i]);
sort(tmp.begin(), tmp.end());
FOR(i, 0, n-1) if(tmp[i] == tmp[i+1]) return false;
return true;
}
int pos = (k-inputSeq[k]+1+n)%n;
rotate(inputSeq, inputSeq+pos, inputSeq+n);
vi tmp;
FOR(i, 0, n) tmp.pb(inputSeq[i]);
sort(tmp.begin(), tmp.end());
FOR(i, 0, n-1) if(tmp[i] == tmp[i+1]) return false;
FOR(i, 0, n){
if(inputSeq[i] <= n and inputSeq[i] != i+1) return false;
}
return true;
}
INT replacement(INT n, INT gondolaSeq[], INT replacementSeq[]){
valid(n, gondolaSeq);
vii seq(n);
FOR(i, 0, n) seq[i] = {gondolaSeq[i], i+1};
sort(&seq[0], &seq[n]);
int j = n+1;
vi ret;
FOR(i, 0, n){
while(seq[i].fst != seq[i].snd) ret.pb(seq[i].snd), seq[i].snd = j++;
}
FOR(i, 0, ret.size()) replacementSeq[i] = ret[i];
return ret.size();
}
int mpow(int a, int b){
if(b==0) return 1;
if(b&1) return a*mpow(a, b-1)%mod;
return mpow(a*a%mod, b>>1);
}
INT countReplacement(INT n, INT inputSeq[]){
if(!valid(n, inputSeq)) return 0;
int res = 1;
sort(inputSeq, inputSeq+n);
int j = n+1;
bool all = 1;
FOR(i, 0, n){
if(inputSeq[i] <= n) { all = 0; continue; }
res = res * mpow(n-i, inputSeq[i]-j) % mod;
j = inputSeq[i]+1;
}
if(all) res = res * n % mod;
return res;
}
/*
signed main(){
int n;
INT seq[NMAX], outSeq[NMAX];
cin >> n;
FOR(i, 0, n) cin >> seq[i];
//int l = replacement(n, seq, outSeq);
//FOR(i, 0, l) cout << outSeq[i] << " ";
//cout << endl;
cout<<countReplacement(n, seq)<<endl;
fast_io();
}*/
