#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define ll long long
const int MOD = 1e9 + 9;
int valid(int n, int arr[]){
set<ll> s, s2;
for(int i = 0; i < n; i++){
if(arr[i] <= n) s.insert((arr[i] - i + n) % n);
s2.insert(arr[i]);
}
return (s2.size() == n && s.size() <= 1);
}
//----------------------
int replacement(int n, int a[], int replacementSeq[])
{
ll st = -1, b[n];
for (ll i = 0; i < n; i++)
if (a[i] <= n)
st = i;
if (st == -1)
iota(b, b + n, 1);
else
{
b[st] = a[st];
for (ll i = st + 1; i < st + n; i++)
b[i % n] = b[(i - 1 + n) % n] % n + 1;
}
ll ptr = 0, mx = max_element(a, a + n) - a;
ll ind[a[mx] + 1];
for (ll i = 0; i <= a[mx]; i++)
ind[i] = -1;
for (ll i = 0; i < n; i++)
ind[a[i]] = i;
for (ll i = n + 1; i <= a[mx]; i++)
if (ind[i] != -1)
replacementSeq[ptr++] = b[ind[i]], b[ind[i]] = i;
else
replacementSeq[ptr++] = b[mx], b[mx] = i;
return ptr;
}
//----------------------
ll binpow(ll a, ll b){
a %= MOD;
ll res = 1;
while(b){
if(b & 1) res = res * a % MOD;
b /= 2;
a = a * a % MOD;
}
return res;
}
int countReplacement(int n, int arr[]){
if(!valid(n, arr)) return 0;
vector<int> v;
for(int i = 0; i < n; i++){
if(arr[i] > n) v.push_back(arr[i]);
}
sort(v.begin(), v.end());
v.insert(v.begin(), n);
ll ans = 1;
for(int i = 1; i < v.size(); i++){
ans = ans * binpow(v.size() - i, v[i] - v[i - 1] - 1) % MOD;
}
if(v.size() - 1 == n) ans = ans * n % MOD;
return ans;
}
