#include "gondola.h"
#include<bits/stdc++.h>
using namespace std;
#define maxn 100005
#define mod 1000000009LL
int n,m,mx;
int a[maxn];
set<int> vis;
map<int,int> s;
long long gpow(long long x,long long y) {
if(y==0) return 1LL;
if(y%2==0) return gpow((x*x)%mod,y/2);
return (gpow(x,y-1)*x)%mod;
}
int valid(int N, int p[]) {
int i, x = 0, val;
n = N;
//Build
for(i=0;i<n;i++) if(p[i]<=n) x = i;
val = p[x];
for(i=0;i<n;i++) a[x] = val, x = (x+1)%n, val = val%n+1;
//Check
for(i=0;i<n;i++) if(p[i]<=n && a[i]!=p[i]) return 0;
//Rep
for(i=0;i<n;i++) {
if(vis.find(p[i])!=vis.end()) return 0;
vis.insert(p[i]);
}
return 1;
}
int replacement(int N, int p[], int res[]) {
int i, x=-1, val;
n = N;
//Build
for(i=0;i<n;i++) if(p[i]<=n) x = i;
if(x==-1) val = 1, x = 0;
else val = p[x];
for(i=0;i<n;i++) a[x] = val, x = (x+1)%n, val = val%n+1;
//Check
for(i=0;i<n;i++) {
mx = max(mx,p[i]);
if(p[i]>n) s[p[i]] = i;
}
m = 0;
for(i=n+1;i<=mx;i++) {
if(s.find(i)!=s.end()) res[m++] = a[s[i]], a[s[i]] = i, s.erase(s.find(i));
else if(s.size()>0) res[m++] = a[s.begin()->second], a[s.begin()->second] = i;
else return 0;
}
return m;
}
int countReplacement(int N, int p[]) {
int i, x=-1, val, cy;
long long ans;
n = N;
//Build
cy = 0;
for(i=0;i<n;i++) if(p[i]<=n) x = i;
if(x==-1) val = 1, x = 0, cy = 1;
else val = p[x];
for(i=0;i<n;i++) a[x] = val, x = (x+1)%n, val = val%n+1;
//Check
for(i=0;i<n;i++) if(p[i]<=n && a[i]!=p[i]) return 0;
//Rep
for(i=0;i<n;i++) {
if(vis.find(p[i])!=vis.end()) return 0;
vis.insert(p[i]);
}
//Check
sort(&p[0],&p[n]);
m = 0;
for(i=0;i<n;i++) if(p[i]>n) m++;
ans = 1;
int last = n;
for(i=0;i<n;i++) {
x = p[i];
if(x<=n) continue;
ans = ((ans*gpow(m,x-last-1))%mod + mod)%mod;
// printf("%d: m = %d\n",x,m);
m--;
last = x;
}
if(cy) ans = ((ans*n)%mod + mod)%mod;
return ans;
}
