#include "gondola.h"
#include "bits/stdc++.h"
using namespace std;
#define FAST ios_base::sync_with_stdio(false); cin.tie(0);
#define pb push_back
#define eb emplace_back
#define ins insert
#define f first
#define s second
#define cbr cerr << "hi\n"
#define mmst(x, v) memset((x), v, sizeof ((x)))
#define siz(x) ll(x.size())
#define all(x) (x).begin(), (x).end()
#define lbd(x,y) (lower_bound(all(x),y)-x.begin())
#define ubd(x,y) (upper_bound(all(x),y)-x.begin())
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); //can be used by calling rng() or shuffle(A, A+n, rng)
inline long long rand(long long x, long long y) { return (rng() % (y+1-x)) + x; } //inclusivesss
string inline to_string(char c) {string s(1,c);return s;} template<typename T> inline T gcd(T a,T b){ return a==0?llabs(b):gcd(b%a,a); }
typedef long long ll;
typedef long double ld;
#define FOR(i,s,e) for(ll i=s;i<=ll(e);++i)
#define DEC(i,s,e) for(ll i=s;i>=ll(e);--i)
typedef pair<ll,ll>pi; typedef pair<ll,pi>spi; typedef pair<pi,pi>dpi;
#define LLINF ((long long)1e18)
#define INF int(1e9+1e6)
#define MAXN (100006)
ll n;
unordered_map<ll,ll>exists,pos;
int valid(int N, int A[]) {
n=N;
ll shift=-1;
FOR(i,0,n-1)--A[i];
FOR(i,0,n-1)if(exists[A[i]])return 0;else exists[A[i]]=1;
FOR(i,0,n-1)if(A[i]<n){
if(~shift){if((i+shift)%n!=A[i])return 0;}
else shift=(A[i]-i+n)%n;
}
return 1;
}
void shifty(int*A){
ll shift=0;
FOR(i,0,n-1)if(A[i]<=n)shift=(A[i]-1-i+n)%n;
vector<ll> B(n);
FOR(i,0,n-1)B[(i+shift)%n]=A[i];
FOR(i,0,n-1)A[i]=B[i];
}
int replacement(int N, int A[], int B[]) {
n=N;
shifty(A);
ll mx=max_element(A,A+n)-A;
FOR(i,0,n-1)pos[A[i]]=i;
ll co=0,val=mx+1;
FOR(i,n+1,A[mx]){
if(pos.count(i) && i!=A[mx]) B[co++]=pos[i]+1;
else B[co++]=val, val=i;
}
return co;
}
ll mod=1e9+9;
int B[MAXN];
int countReplacement(int N, int A[]) {
n=N;
FOR(i,0,n-1)B[i]=A[i];
ll ans=valid(n,B);
vector<ll> hmm;
FOR(i,0,n-1)if(A[i]>n)hmm.eb(A[i]);
sort(all(hmm));
auto qexp=[&](ll x,ll e){
ll sum=1;
while(e){
if(e&1)sum*=x,sum%=mod;
x*=x,x%=mod;
e>>=1;
}
return sum;
};
// assert(siz(hmm)<n);
FOR(i,0,siz(hmm)-1){
if(hmm[i]-1-(i?hmm[i-1]:n) > 0) {
ll p=hmm[i]-1-(i?hmm[i-1]:n);
ans *= qexp(siz(hmm) - i, p), ans %= mod;
}
}
if(siz(hmm)==n) ans*=n, ans%=mod;
return ans;
}
