#include <bits/stdc++.h>
#include <gondola.h>
#define loop(i, a, b) for(long long i=a;i<b;i++)
#define pool(i, a, b) for(long long i=a-1;i>=b;i--)
#define fore(i, a) for(auto&& i:a)
#define fi first
#define se second
#define ps(a) push_back(a)
#define pb(a) pop_back(a)
#define sc scanf
#define vc vector
#define pa pair<ll, ll>
#define ll long long
#define lb lower_bound
#define ub upper_bound
#define all(a) a.begin(), a.end()
#define llmax LLONG_MAX/2
#define llmin -LLONG_MAX/2
using namespace std;
#define mn 200100
#define pa pair<ll, ll>
#define ld long double
#define k 450
int valid(int n, int inputSeq[]){
vc<pa> tes;
map<ll, ll> cnt;loop(i, 0, n) cnt[inputSeq[i]]++;
fore(v, cnt) if(v.se>1) return 0;
loop(i, 0, n) if(inputSeq[i]<=n)tes.ps(make_pair(i, inputSeq[i]));
if(tes.size()==0) return 1;
ll siz=tes.size();
loop(i, 0, tes.size()) if((tes[(i+1)%siz].fi-tes[i].fi+n)%n!=(tes[(i+1)%siz].se-tes[i%siz].se+n)%n){
return 0;
}
return 1;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[]){
ll zac=1, cnt=0;
map<ll, ll> poi;
loop(i, 0, n){
if(gondolaSeq[i]<=n) zac=(gondolaSeq[i]-i+n)%n;
else poi[gondolaSeq[i]]=i;
}
if(poi.size()==0) return 0;
vc<ll> cur(n, 0);
loop(i, 0, n){
cur[i]=(zac+i)%n;
if(cur[i]==0) cur[i]=n;
}
loop(j, n+1, poi.begin()->fi+1) replacementSeq[cnt++]=cur[poi.begin()->se], cur[poi.begin()->se]=j;
for(auto v=poi.begin();v!=poi.end();++v){
auto ne=v; ++ne;
if(ne==poi.end()) break;
loop(j, v->fi+1, ne->fi+1) replacementSeq[cnt++]=cur[ne->se], cur[ne->se]=j;
}
auto bac=poi.end();bac--;
return cnt;
}
ll mod=1000000009;
ll pot(ll ba, ll ex){
ll ret=1;
while(ex){
if(ex&1) ret*=ba;
ba*=ba;
ex/=2;
ret%=mod;
ba%=mod;
}
return ret;
}
int countReplacement(int n, int inputSeq[]){
if(!valid(n, inputSeq)) return 0;
ll ans=1;
vc<ll> srt;
loop(i, 0, n) if(inputSeq[i]>n) srt.ps(inputSeq[i]);
if(srt.size()==0) return 1;
srt.ps(n);
sort(all(srt));
loop(i, 0, srt.size())srt[i]-=n+i;
ll siz=(ll)srt.size();
loop(i, 1, (ll)srt.size()){
if(srt[i]-srt[i-1]) ans*=pot(siz-i, srt[i]-srt[i-1]);
ans%=mod;
}
return ans;
}
