#include "gondola.h"
#include <bits/stdc++.h>
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define ALL(x) x.begin(), x.end()
using namespace std;
typedef long long LL;
typedef vector<int> vi;
typedef pair<int,int> pii;
int valid(int n, int inputSeq[]){
vi a(inputSeq, inputSeq + n);
// handle whether all values are unique
vi b(a.begin(), a.end());
sort(ALL(b)); b.erase(unique(ALL(b)), b.end());
if (b.size() != a.size()) return 0;
// handle min element
vi::iterator mnit = min_element(a.begin(), a.end());
int mn = *mnit, pos = mnit - a.begin();
if (mn >= n) return 1;
// rotate elements so that min is at first position.
// now index i will be original position of (mn + i - 1)%n + 1;
rotate(a.begin(), a.begin() + pos, a.end());
// validity check
for (int i = 0; i < n; i++){
if (a[i] > n) continue;
if (a[i] != ((mn + i - 1) % n + 1)) return 0;
}
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[]){
vi a(gondolaSeq, gondolaSeq + n);
// get length
int len = (*max_element(a.begin(), a.end())) - n;
vi::iterator mnit = min_element(a.begin(), a.end());
int mn = *mnit, pos = mnit - a.begin();
if (mn < n){
rotate(a.begin(), a.begin() + pos, a.end());
} else {
pos = 0;
}
vector<pii> rep; // to be replaced
for (int i = 0; i < n; i++){
int oriNum = mn < n ? ((mn + i - 1) % n) + 1 : i+1;
if (a[i] > n || a[i] != oriNum){
rep.eb(a[i], oriNum);
}
}
sort(rep.begin(), rep.end());
int cur = n+1, idx = 0;
for (int i = 0; i < rep.size(); i++){
int prv = rep[i].se;
while (cur <= rep[i].fi){
replacementSeq[idx++] = prv;
prv = cur;
cur++;
}
}
return len;
}
//----------------------
const LL mod = 1e9 + 9;
LL fpow(LL b, LL e, LL m = mod){
LL r = 1;
for (; e > 0; e >>= 1){
if (e&1) (r *= b) %= m;
(b *= b) %= m;
}
return r;
}
int countReplacement(int n, int inputSeq[]){
if (!valid(n, inputSeq)) return 0;
vi a(inputSeq, inputSeq + n);
vi::iterator mnit = min_element(a.begin(), a.end());
int mn = *mnit, pos = mnit - a.begin();
rotate(a.begin(), a.begin() + pos, a.end());
vector<pii> rep;
LL tot = 1;
int cur = n;
for (int i = 0; i < n; i++){
int oriNum = (mn + i - 1) % n + 1;
if (a[i] != oriNum)
rep.eb(a[i], oriNum);
else cur--;
}
sort(rep.begin(), rep.end());
int prv = n;
for (pii p : rep){
(tot *= fpow(cur, p.fi - prv - 1)) %= mod;
cur--;
prv = p.fi;
}
if (mn > n){
(tot *= n) %= mod;
}
return tot;
}
