#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
const int N=100006;
typedef long long ll;
const ll MOD=1000000009;
map<int,bool> used;
ll pwr(int num,int power){
if (power==0) return 1;
if (power==1) return num;
ll sqr=pwr(num,power/2);
ll ans=sqr*sqr;
ans%=MOD;
if (power%2){
ans*=num;
ans%=MOD;
}
return ans;
}
int valid(int n, int inSeq[])
{
int start=-1;
for (int i=0;i<n;i++){
if (used[inSeq[i]]){
return 0;
}
used[inSeq[i]]=true;
if (inSeq[i]<=n){
if (start!=-1 && (n+i-inSeq[i]+1)%n!=start){
return 0;
}
start=(n+i-inSeq[i]+1)%n;
}
}
return 1;
}
int replacement(int n, int inSeq[], int finalAns[])
{
//cout<<n<<endl;
if (n==0) return 0;
int start=0;
for (int i=0;i<n;i++){
if (inSeq[i]<=n){
start=(n+i-inSeq[i]+1)%n;
}
}
vector<pair<int,int> > v;
for (int i=0;i<n;i++){
v.push_back({inSeq[i],(n+i-start)%n+1});
}
sort(v.begin(),v.end());
int ansLength=0;
int curGondola=n+1;
for (int i=0;i<n;i++){
//cout<<i<<endl;
if (v[i].second==v[i].first)continue;
finalAns[ansLength++]=v[i].second;
curGondola++;
//cout<<v[i].first<<endl;
while (curGondola!=v[i].first+1){
//cout<<ansLength<<" ";
finalAns[ansLength++]=curGondola-1;
curGondola++;
}
}
return ansLength;
}
int countReplacement(int n, int inSeq[])
{
if (!valid(n,inSeq)) return 0;
bool untilN=false;
for (int i=0;i<n;i++){
if (inSeq[i]<=n){
untilN=true;
}
}
vector<int> v;
for (int i=0;i<n;i++){
v.push_back(inSeq[i]);
}
sort(v.begin(),v.end());
ll finalAns=1;
int curGondola=n+1;
for (int i=0;i<n;i++){
if (v[i]<=n)continue;
//cout<<finalAns<<endl;
finalAns*=pwr(n-i,v[i]-curGondola);
finalAns%=MOD;
curGondola=v[i]+1;
}
if (!untilN){
finalAns*=n;
finalAns%=MOD;
}
return finalAns;
}
/*
int gondolaSequence[100001];
int replacementSequence[250001];
int main()
{
//freopen("05-007.in","r",stdin);
int i, n, tag;
int nr;
assert(scanf("%d", &tag)==1);
assert(scanf("%d", &n)==1);
for(i=0;i< n;i++)
assert( scanf("%d", &gondolaSequence[i]) ==1);
switch (tag){
case 1: case 2: case 3:
printf("%d\n", valid(n, gondolaSequence));
break;
case 4: case 5: case 6:
nr = replacement(n, gondolaSequence, replacementSequence);
printf("%d ", nr);
if (nr > 0)
{
for (i=0; i<nr-1; i++)
printf("%d ", replacementSequence[i]);
printf("%d\n", replacementSequence[nr-1]);
}
else printf("\n");
break;
case 7: case 8: case 9: case 10:
printf("%d\n", countReplacement(n, gondolaSequence));
break;
}
return 0;
}
*/
