#include "gondola.h"
#define MOD 1000000009
#include<algorithm>
using namespace std;
#define MX 200001
int d[MX],check[MX],D[MX];
int l,ind;
int valid(int n, int inputSeq[]){
int i,cnt=0,ind;
for(i=0;i<n;i++){check[i]=inputSeq[i];}
sort(check,check+n);
for(i=1;i<n;i++){
if(check[i]==check[i-1]){return 0;}
}
for(i=0;i<n;i++){
if(inputSeq[i]<=n){
cnt=1;
ind=(inputSeq[i]-1-i)+n;
ind%=n;
break;
}
}
if(cnt==0){return 1;}
for(i=0;i<n;i++){
d[(ind+i)%n]=inputSeq[i];
}
for(i=0;i<n;i++){
if(d[i]<=n&&d[i]!=(i+1)){
return 0;
}
}
return 1;
}
struct DT{
int x,y;
bool operator<(const DT&r)const{
return r.x>x;
}
}make[MX];
int replacement(int n, int gondolaSeq[], int replacementSeq[]){
int ll=0,o=n,flag=0,indin,i,j;
for(i=0;i<n;i++){
if(gondolaSeq[i]<=n){
flag=1;
indin=gondolaSeq[i];
break;
}
}
if(flag==0){indin=1;}
for(j=i;j<i+n;j++){
make[j%n].x=gondolaSeq[j%n];
if(indin>n){indin-=n;}
make[j%n].y=indin++;
}
sort(make,make+n);
for(i=0;i<n;){
if(make[i].y>=make[i].x){
i++;
continue;
}
replacementSeq[ll++]=make[i].y;
make[i].y=++o;
}
return ll;
}
long long int p,pp;
long long int a[33];
//----------------------
long long int calc(int x,int y){//x의 y승
int i;
a[0]=x%MOD;
if(y==0){
return 1;
}
for(i=1;i<=31;i++){
if(((long long int)1<<i)>y){break;}
p=(a[i-1]*a[i-1]);
a[i]=p%MOD;
}
p=1;
for(i=0;i<=31;i++){
if(((long long int)1<<i)>y){break;}
if((y&((long long int)1<<i))!=0){
p=p*a[i];
p=p%MOD;
}
}
return p%MOD;
}
int countReplacement(int n, int inputSeq[]){
int o=n,i,flag;
long long int lll=0;
pp=1;
flag=0;
lll=0;
if(valid(n,inputSeq)==0){return 0;}
for(i=0;i<n;i++){
if(inputSeq[i]>n){
D[lll++]=inputSeq[i];
}
else{flag=1;}
}
sort(D,D+lll);
pp=1;
for(i=0;i<lll;i++){
pp=(pp*calc(lll-i,D[i]-o-1))%MOD;
o=D[i];
pp%=MOD;
}
if(flag==0){
pp*=lll;
pp%=MOD;
}
pp=pp%MOD;
return pp;
}
