#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef pair <int, int> pii;
#define precision(n) fixed << setprecision(n)
#define pb push_back
#define ub upper_bound
#define lb lower_bound
#define mp make_pair
#define eps (double)1e-9
#define PI 2*acos(0.0)
#define endl "\n"
#define sz(v) int((v).size())
#define all(v) v.begin(),v.end()
#define rall(v) v.rbegin(),v.rend()
#define do_not_disturb ios::sync_with_stdio(0);cin.tie(0);cout.tie(0);
const ll mod = 1e9+9;
ll mult(ll a, ll b){
a = ((a%mod)+mod)%mod;
b = ((b%mod)+mod)%mod;
return (a*b)%mod;
}
ll binpow(ll a, ll b){
ll res = 1;
while(b){
if(b&1) res = mult(res, a);
a = mult(a, a);
b >>= 1;
}
return res;
}
int valid(int n, int s[]){
int in = -1, flag = 1, i;
map <int, int> vis;
for(i = 0; i < n; i++){
if(vis[s[i]]){
flag--;
break;
}
vis[s[i]]++;
if(in == -1 && s[i] <= n){
in = s[i];
}
else if(s[i] <= n && in != s[i]){
flag--;
break;
}
in = (in == -1 ? in : (in+1 > n ? 1 : in+1));
}
return flag;
}
//----------------------
int replacement(int n, int gon[], int repl[]){
int i, num = 0;
vector <int> prev(n);
iota(all(prev), 1);
int in = -1, j;
for(i = 0; i < n; i++){
if(in == -1 && gon[i] <= n){
in = gon[i];
j = i;
break;
}
}
if(in != -1){
for(i = j; i < n; i++){
prev[i] = in;
in = (in == n ? 1 : in+1);
}
for(i = 0; i < j; i++){
prev[i] = in;
in = (in == n ? 1 : in+1);
}
}
vector <pii> bigger;
for(i = 0; i < n; i++){
if(gon[i] > n){
bigger.pb({gon[i], i});
}
}
int op = n;
sort(all(bigger));
for(auto to : bigger){
for(j = op; j < to.first; j++){
repl[num] = prev[to.second];
num++;
prev[to.second] = j+1;
}
op = to.first;
}
return num;
}
//----------------------
int countReplacement(int n, int gon[]){
ll res = 1;
if(!valid(n, gon)){
return 0;
}
vector <int> bigger;
for(int i = 0; i < n; i++){
if(gon[i] > n){
bigger.pb(gon[i]);
}
}
sort(all(bigger));
int prev = n;
for(auto to : bigger){
auto it = ub(all(bigger), prev)-bigger.begin();
ll diff = to-prev-1;
res = mult(res, binpow(ll(sz(bigger)-it), diff));
prev = to;
}
return res*(sz(bigger) == n ? n : 1);
}
