#include "gondola.h"
#include <iostream>
#include <vector>
#include <algorithm>
using namespace std;
using ll = long long;
int valid(int n, int inputSeqArray[])
{
vector<int> inputSeq(n);
for (int i=0; i<n; i++) inputSeq[i] = inputSeqArray[i];
int mini = 1e9;
int min_idx;
for (int i=0; i<n; i++){
if (inputSeq[i] < mini){
mini = inputSeq[i];
min_idx = i;
}
}
int needed_val = mini;
for (int i=min_idx; i<n; i++){
if (inputSeq[i] <= n){
if (inputSeq[i] != needed_val) return false;
}
needed_val++;
}
for (int i=0; i<min_idx; i++){
if (inputSeq[i] <= n){
if (inputSeq[i] != needed_val) return false;
}
needed_val++;
}
sort(inputSeq.begin(), inputSeq.end());
for (int i=1; i<n; i++){
if (inputSeq[i] == inputSeq[i-1]) return false;
}
return true;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
vector<int> originalSeq(n);
int idx = 0;
for (int i=0; i<n; i++){
if (gondolaSeq[i] <= n){
idx = i;
break;
}
}
if (gondolaSeq[idx] > n) originalSeq[idx] = 1;
else originalSeq[idx] = gondolaSeq[idx];
for (int i=idx+1; i<n; i++){
originalSeq[i] = originalSeq[i-1]+1;
if (originalSeq[i] > n) originalSeq[i] -= n;
}
for (int i=idx-1; i>=0; i--){
originalSeq[i] = originalSeq[i+1]-1;
if (originalSeq[i] < 1) originalSeq[i] += n;
}
//for (int x : originalSeq) cerr << x << " ";
//cerr << endl;
vector<pair<int, int>> replacedGondolas;
int max_val = 0;
for (int i=0; i<n; i++){
max_val = max(max_val, gondolaSeq[i]);
if (gondolaSeq[i] > n){
replacedGondolas.push_back({gondolaSeq[i], i});
}
}
sort(replacedGondolas.begin(), replacedGondolas.end());
idx = 0;
for (int i=n+1; i<=max_val; i++){
int replace_idx = replacedGondolas[idx].second;
replacementSeq[i-(n+1)] = originalSeq[replace_idx];
originalSeq[replace_idx] = i;
if (i == replacedGondolas[idx].first) idx++;
}
return max_val-n;
}
//----------------------
const ll MOD = 1e9+9;
int countReplacement(int n, int inputSeq[])
{
bool validSeq = valid(n, inputSeq);
if (!validSeq) return 0;
ll res = 1;
vector<int> replacedGondolas;
int max_val = 0;
for (int i=0; i<n; i++){
max_val = max(max_val, inputSeq[i]);
if (inputSeq[i] > n){
replacedGondolas.push_back(inputSeq[i]);
}
}
sort(replacedGondolas.begin(), replacedGondolas.end());
ll remainingGondolas = replacedGondolas.size();
if (remainingGondolas == n) res *= n;
int idx = 0;
for (int i=n+1; i<=max_val; i++){
if (replacedGondolas[idx] == i){
idx++;
remainingGondolas--;
}
else{
res = (res * remainingGondolas) % MOD;
}
}
return res;
}
