/*input
10
4
4 8 2 6
*/
#include "gondola.h"
#include<bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#pragma GCC optimize("unroll-loops,no-stack-protector")
//order_of_key #of elements less than x
// find_by_order kth element
#define ll long long
#define ld long double
#define pii pair<int,int>
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> indexed_set;
#define f first
#define s second
#define pb push_back
#define REP(i,n) for(int i=0;i<n;i++)
#define REP1(i,n) for(int i=1;i<=n;i++)
#define FILL(n,x) memset(n,x,sizeof(n))
#define ALL(_a) _a.begin(),_a.end()
#define sz(x) (int)x.size()
#define SORT_UNIQUE(c) (sort(c.begin(),c.end()), c.resize(distance(c.begin(),unique(c.begin(),c.end()))))
#define MP make_pair
const int maxn=1e5+5;
const ll INF64=4e12;
const int INF=0x3f3f3f3f;
const ll MOD=1e9+9;
const ld PI=acos(-1);
const ld eps=1e-9;
#define lowb(x) x&(-x)
#define MNTO(x,y) x=min(x,(__typeof__(x))y)
#define MXTO(x,y) x=max(x,(__typeof__(x))y)
ll mult(ll a,ll b){
return ((a%MOD)*(b%MOD))%MOD;
}
ll mypow(ll a,ll b){
if(b<=0) return 1;
ll res=1LL;
while(b){
if(b&1){
res=mult(res,a);
}
a=mult(a,a);
b>>=1;
}
return res;
}
int valid(int n, int arr[]){
vector<int> v;
REP(i,n) v.pb(arr[i]);
int x=sz(v);
SORT_UNIQUE(v);
if(sz(v)!=x){
return 0;
}
int pv=arr[0];
int st=1;
while(st<n and pv>n){
pv=arr[st];
++st;
}
if(st==n){
return 1;
}
--st;
st+=n;
st%=n;
int i=(st+1)%n;
while(i!=st){
pv++;
if(pv==n+1) pv=1;
//cout<<i<<' '<<pv<<'\n';
if(arr[i]<=n and arr[i]!=pv){
return 0;
}
i++;
i%=n;
}
return 1;
}
//----------------------
int supposed[maxn];
int replacement(int n, int arr[], int ans[])
{
int pv=arr[0];
int st=1;
while(st<n and pv>n){
pv=arr[st];
++st;
}
vector<pii> v;
if(st==n){
v.pb({arr[0],1});
pv=1;
st=1;
}
--st;
st+=n;
st%=n;
int i=(st+1)%n;
while(i!=st){
pv++;
if(pv==n+1) pv=1;
//cout<<i<<' '<<pv<<'\n';
if(arr[i]!=pv){
v.pb({arr[i],pv});
}
i++;
i%=n;
}
sort(ALL(v));
int ptr=0;
int cur=n+1;
REP(j,sz(v)){
ans[ptr++]=v[j].s;
while(cur<v[j].f){
ans[ptr++]=cur++;
}
++cur;
}
return ptr;
}
//----------------------
int countReplacement(int n, int arr[])
{
if(!valid(n,arr)){
return 0;
}
vector<int> v;
REP(i,n){
if(arr[i]>n) v.pb(arr[i]);
}
sort(ALL(v));
ll ans=1;
int pv=n;
REP(i,sz(v)){
ans=mult(ans,mypow(sz(v)-i,v[i]-pv-1));
pv=v[i];
}
if(sz(v)==n) ans=mult(ans,n);
return (int)ans;
}
