#include <algorithm>
#include <bitset>
#include <cassert>
#include <chrono>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <ctime>
#include <deque>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <numeric>
#include <queue>
#include <random>
#include <ratio>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#include <climits>
#include <ext/pb_ds/assoc_container.hpp>
// #include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/trie_policy.hpp>
#include <gondola.h>
#define ll long long
#define ld long double
#define mp make_pair
#define pb push_back
#define in insert
#define vll vector<ll>
#define endl "\n"
#define pll pair<ll,ll>
#define f first
#define s second
// #define int ll
#define sz(x) (ll)x.size()
#define all(x) (x.begin(),x.end())
using namespace std;
using namespace __gnu_pbds;
typedef tree<int,null_type,less<int>,rb_tree_tag,tree_order_statistics_node_update> os;
const ll INF = 1e18;
const ll N =(1e5+5); // TODO : change value as per problem
const ll MOD = 1e9+9;
ll power(ll a, ll b) //a is base, b is exponent
{
if(b==0)
return 1;
if(b==1)
return a;
if(b%2 == 1)
return (power(a,b-1)*a)%MOD;
ll q = power(a,b/2);
return (q*q)%MOD;
}
int valid(int n, int a[]){
ll idx = 0;
bool original = 0;
for(int i =0;i<n;i++){
if(a[i] <= n){
idx =i;
original = true;
break;
}
}
if(original == false){
set<ll> se;
for(int i = 0;i<n;i++) se.in(a[i]);
if(sz(se) == n){
return 1;
}
else return 0;
}
int b[n];
vector<int> ans;
vector<pair<int,int>> gg;
ll count = 1;
ll nxt = a[idx];
if(original == false) nxt = 1;
// cout << idx << endl;
while(count <= n){
b[idx] = nxt;
nxt++;
idx++;
if(nxt > n) nxt = 1;
if(idx >= n) idx = 0;
count++;
}
set<ll> se;
for(int i =0;i<n;i++){
if(a[i] <= n && b[i] != a[i]){
return 0;
}
else
se.in(a[i]);
}
if(sz(se) != n) return 0;
return 1;
}
int replacement(int n, int a[], int replacementSeq[]) {
ll idx = 0;
bool original = 0;
for(int i =0;i<n;i++){
if(a[i] <= n){
idx =i;
original = true;
break;
}
}
int b[n];
vector<int> ans;
vector<pair<int,int>> gg;
ll count = 1;
ll nxt = a[idx];
if(original == false) nxt = 1;
// cout << idx << endl;
while(count <= n){
b[idx] = nxt;
nxt++;
idx++;
if(nxt > n) nxt = 1;
if(idx >= n) idx = 0;
count++;
}
ll sp = n+1;
// for(int i =0;i<n;i++) cout << b[i] << " ";cout<<endl;
for(int i =0;i<n;i++){
if(a[i] > n)
gg.pb({a[i],b[i]});
}
sort(gg.begin(),gg.end());
for(int i = 0;i<sz(gg);i++){
ans.pb(gg[i].s);
ll x = sp;
while(x != gg[i].f){
ans.pb(x);
x++;
}
sp = gg[i].f+1;
}
// for(int i = 0;i<sz(ans);i++) cout<<ans[i]<<" ";cout<<endl;
for(int i = 0;i<sz(ans);i++) replacementSeq[i] = ans[i];
return sz(ans);
}
int countReplacement(int n, int inputSeq[]) {
//cout << "QQA\n";
if(!valid(n,inputSeq)) return 0;
//cout<<"QQA\n";
ll special = 0;
vll v;
for(int i =0;i<n;i++){
if(inputSeq[i] > n){
special += 1;
v.pb(inputSeq[i]);
}
}
if(special == 0) return 1;
ll ans = n;
if(special != n) ans = 1;
sort(v.begin(),v.end());
ll maxi = n+1;
ll r = sz(v);
for(int i = 0;i<sz(v);i++){
ans = (ans * power(r,v[i]-maxi))%MOD;
// maxi = v[i];
r--;
maxi = v[i]+1;
}
return ans;
}
