#include "gondola.h"
#include <bits/stdc++.h>
int i;
struct A{
int val,ind;
}data[100005];
bool cmp(A aa,A bb){return aa.val<bb.val;}
long long X=1e9+9;
long long f(long long p,long long q)
{
if(q==0)return 1ll;
if(q==1)return p;
long long O=f(p,q/2);
O=O*O%X;
if(q%2)return O*p%X;
return O;
}
int valid(int n, int inputSeq[])
{
int ST=-1,st,C=1;
std::map<int,int>ch;
for(i=0;i<n;i++)
{
if(ch[inputSeq[i]]==1){C=0;break;}
ch[inputSeq[i]]=1;
}
for(i=0;i<n;i++)
{
if(inputSeq[i]<=n)
{
st=i-inputSeq[i]+1;st=(st+n)%n;
if(ST==-1)ST=st;
else if(ST!=st){C=0;break;}
}
}
return C;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int ST=0,ba,sz=0,ans=0;
for(i=0;i<n;i++)
{
if(gondolaSeq[i]<=n)ST=(i-gondolaSeq[i]+1+n)%n;
else data[sz++]={gondolaSeq[i],i};
}
std::sort(data,data+sz,cmp);
ba=n;
for(i=0;i<sz;i++)
{
replacementSeq[ans++]=(data[i].ind-ST+n)%n+1;
for(int j=ba+1;j<data[i].val;j++)
{
replacementSeq[ans++]=j;
}
ba=data[i].val;
}
return ans;
}
//----------------------
int countReplacement(int n, int inputSeq[])
{
if(valid(n,inputSeq)==0)return 0;
int ST=-1,ba,sz=0;
long long ans=1ll;
for(i=0;i<n;i++)
{
if(inputSeq[i]<=n)ST=(i-inputSeq[i]+1+n)%n;
else data[sz++]={inputSeq[i],i};
}
if(ST==-1)ST=0,ans*=n;
std::sort(data,data+sz,cmp);
ba=n;
for(i=0;i<sz;i++)
{
ans*=f(sz-i,data[i].val-ba-1);
ans%=X;
ba=data[i].val;
}
return ans;
}
