#include "gondola.h"
#include<bits/stdc++.h>
using namespace std;
#define ff first
#define ss second
#define all(x) (x).begin(), (x).end()
#define pb push_back
typedef int64_t lld;
typedef pair<int, int> pii;
typedef long double ld;
int valid(int n, int inputSeq[]) {
set<int> uses;
for(int i = 0; i < n; i++)if(inputSeq[i] <= n){
rotate(inputSeq, inputSeq+i, inputSeq+n);
if(inputSeq[0] != 1) rotate(inputSeq, inputSeq + (n-inputSeq[0]+1), inputSeq + n);
break;
}
for(int i = 0; i < n; i++)
if(inputSeq[i] == i+1) continue;
else if(inputSeq[i] <= n)return 0; else if(uses.count(inputSeq[i])) return 0; else uses.insert(inputSeq[i]);
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[]) {
map<int, int> mp;
for(int i = 0; i < n; i++)if(gondolaSeq[i] <= n){
rotate(gondolaSeq, gondolaSeq+i, gondolaSeq+n);
if(gondolaSeq[0] != 1) rotate(gondolaSeq, gondolaSeq + (n-gondolaSeq[0]+1), gondolaSeq + n);
break;
}
for(int i = 0; i < n; i++)if(gondolaSeq[i] > n)mp[gondolaSeq[i]] = i+1;
int cur = 0;
for(auto i: mp){
int l = i.ss;
while(cur+n < i.ff)
replacementSeq[cur++] = l, l = n+cur;
}
return cur;
}
//----------------------
const int mod = 1000000009;
inline int fpow(lld a, int b){
lld ans = 1;
do if(b&1) ans = ans*a%mod;
while(a = a*a%mod, b>>=1);
return (int)ans;
}
int countReplacement(int n, int inputSeq[]) {
vector<int> v;
if(!valid(n, inputSeq))return 0;
for(int i = 0; i < n; i++)if(inputSeq[i] > n)v.pb(inputSeq[i]);
sort(all(v));
lld ans = 1;
for(int i = 0; i < (int)v.size(); i++)
ans = ans*fpow((int)v.size()-i, (v[i]-(i?v[i-1]:n)-1))%mod;
return (int)(ans*((int)v.size() == n? n:1)%mod);
}
