#include "gondola.h"
#include<bits/stdc++.h>
using namespace std;
#define MOD 1000000009
#define ll long long
int valid(int n, int a[]){
map<int, bool> used;
for(int i=0;i<n;i++){
if(used[a[i]]) return 0;
used[a[i]] = true;
}
int s = 0;
for(int i=0;i<n;i++){
if(a[i]<=n){
s = i;
break;
}
}
for(int i=0;i<n;i++){
if(a[i]<=n && (a[i]+(s-i) - 1 + n)%n + 1 != a[s]) return 0; }
return 1;
}
//----------------------
int replacement(int n, int a[], int ans[]){
int apos=-1, av;
int maxf=0;
int minf = 0;
unordered_map<int, int> m;
for(int i=0;i<n;i++){
if(a[i]<=n) apos = i, av=a[i];
else m[a[i]] = i+1;
maxf = max(maxf, a[i]);
if(a[minf]>a[i]) minf = i;
}
if(apos==-1){
apos = minf;
av = 1;
}
queue<int> q;
int l=0;
for(int i=n+1;i<=maxf;i++){
if(m[i]){
int c = l - 1;
ans[l] = (n + av - (apos - m[i] + 1) - 1) % n + l - c;
l++;
//cout<<apos<<" "<<m[i]<<" "<<av<<endl;
while(!q.empty()){
ans[l] = q.front();
q.pop();
l++;
}
}
else q.push(i);
}
return l;
}
//----------------------
ll mpow(ll a, ll b){
if(b==0) return 1;
if(b==1) return a;
ll z = mpow(a, b/2);
z*=z;
z%=MOD;
if(b%2) z*=a;
z%=MOD;
return z;
}
int countReplacement(int n, int a[]){
if(!valid(n, a)) return 0;
int act=-1;
int un=0;
for(int i=0;i<n;i++){
if(a[i]<=n) act = i;
else un++;
}
sort(a, a+n);
ll ans=1;
if(act==-1) ans*=n;
ll prev = n+1;
for(int i=0;i<n-1 && un>=1;i++){
if(a[i]<=n) continue;
//cout<<un<<" "<<mpow(un, a[i+1]-a[i]-1)<<" "<<a[i]<<" "<<a[i+1]<<endl;
ans *= mpow(un, a[i]-prev);
ans%=MOD;
prev = a[i]+1;
un--;
}
return ans;
}
