#include "gondola.h"
#include<bits/stdc++.h>
using namespace std;
#define prev(i) ((i-1+n)%n)
typedef long long ll;
typedef long double ld;
const ll inf = 1e18;
const ll mod = 1e9+9;
#define pii pair<int,int>
#define pll pair<ll,ll>
#define vi vector<int>
#define vll vector<ll>
#define rep(i, a, b) for(int i = (a);i<(b);i++)
#define repn(i, a, b) for(int i = (a);i>=(b);i--)
#define ss second
#define ff first
#define mkp make_pair
#define pb push_back
#define all(x) (x).begin(), (x).end()
int valid(int n, int a[])
{
int cnt = a[0]-1;
for(int i = 1;i<n-cnt;i++) {
if(a[i] != a[i-1]+1) {
return 0;
}
}
for(int i = n-cnt+1;i<n;i++) {
if(a[i]!=a[i-1]+1)return 0;
}
if(cnt==0)return 1;
if(a[0] != a[n-1]+1)return 0;
return 1;
return -1;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int cnt=0;
for(int i = 0;i<n;i++) {
if(gondolaSeq[i]>n)cnt++;
}
if(cnt == 0)return 0;
else if(cnt == n) {
vector<pair<int,int>> res;
res.push_back(mkp(n,n));
for(int i = 0;i<n;i++) {
res.push_back(mkp(gondolaSeq[i], i+1));
}
sort(res.begin(), res.end());
vector<int> ans;
for(int i=1;i<(int)res.size();i++) {
ans.push_back(res[i].second);
for(int j = res[i-1].first;j<res[i].first-1;j++) {
ans.push_back(j+1);
}
}
for(int i=0;i<(int)ans.size();i++) {
replacementSeq[i]=ans[i];
}
return (int)ans.size();
}
else {
vector<pair<int,int>> res;
res.push_back(make_pair(n,n));
for(int i = 0;i<n;i++) {
if(gondolaSeq[i] > n and gondolaSeq[prev(i)]<=n) {
int tmp = gondolaSeq[i];
gondolaSeq[i] = (gondolaSeq[prev(i)]%n)+1;
res.push_back(make_pair(tmp, gondolaSeq[i]));
}
}
for(int i = 0;i<n;i++) {
if(gondolaSeq[i] > n and gondolaSeq[prev(i)]<=n) {
int tmp = gondolaSeq[i];
gondolaSeq[i] = (gondolaSeq[prev(i)]%n)+1;
res.push_back(make_pair(tmp, gondolaSeq[i]));
}
}
sort(res.begin(), res.end());
vector<int> ans;
for(int i=1;i<(int)res.size();i++) {
ans.push_back(res[i].second);
for(int j = res[i-1].first;j<res[i].first-1;j++) {
ans.push_back(j+1);
}
}
for(int i=0;i<(int)ans.size();i++) {
replacementSeq[i]=ans[i];
}
return (int)ans.size();
}
return 0;
}
int countReplacement(int n, int inputSeq[])
{
int mx = 0;
rep(i, 0, n)mx = max(mx, inputSeq[i]);
ll ans=1;
rep(i, n+1, mx+1) {
ll cnt = 0;
bool check=false;
rep(j, 0, n) {
if(inputSeq[j] == i)check=true;
else if(inputSeq[j] > i)cnt++;
}
if(check)cnt=1;
ans*=cnt;
ans%=mod;
}
int gondolaSeq[n];
rep(i, 0, n)gondolaSeq[i]=inputSeq[i];
vector<pair<int,int>> res;
res.push_back(make_pair(n,n));
for(int i = 0;i<n;i++) {
if(gondolaSeq[i] > n and gondolaSeq[prev(i)]<=n) {
int tmp = gondolaSeq[i];
gondolaSeq[i] = (gondolaSeq[prev(i)]%n)+1;
res.push_back(make_pair(tmp, gondolaSeq[i]));
}
}
for(int i = 0;i<n;i++) {
if(gondolaSeq[i] > n and gondolaSeq[prev(i)]<=n) {
int tmp = gondolaSeq[i];
gondolaSeq[i] = (gondolaSeq[prev(i)]%n)+1;
res.push_back(make_pair(tmp, gondolaSeq[i]));
}
}
if(!valid(n, gondolaSeq))return 0;
return ans;
}
