#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define sp " "
#define endl "\n"
#define pb push_back
#define pii pair<int, int>
#define st first
#define nd second
#define mid (l + r) / 2
#define LL node * 2
#define RR node * 2 + 1
#define fileio() freopen("input.txt", "r", stdin), freopen("output.txt", "w", stdout)
#define fastio() cin.tie(0), ios_base::sync_with_stdio(0)
#define ll long long
#define MAXN 200005
const int modulo = 1e9+9;
const ll INF = 2e18 + 7;
int valid(int n, int inputSeq[])
{
set<int> s;
vector<int> v(n, 0);
for (int i = 0; i < n; i++){
int curr = inputSeq[i];
if (curr <= n) v[i] = curr;
s.insert(curr);
}
if (s.size() < n) return 0;
int todo = -1;
for (int i = 0; i < n; i++)
if (v[i] != 0) todo = i;
if (todo == -1) return 1;
vector<int> res(n, 0);
int it = todo, val = v[todo];
do{
res[it] = val;
val++, it++;
it %= n;
val = (val - 1) % n + 1;
}while(it != todo);
for (int i = 0; i < n; i++)
if (v[i] != 0 && res[i] != v[i]) return 0;
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
vector<int> v(n, 0);
for (int i = 0; i < n; i++){
int curr = gondolaSeq[i];
if (curr <= n) v[i] = curr;
}
int todo = -1;
for (int i = 0; i < n; i++)
if (v[i] != 0) todo = i;
vector<int> res(n, 0);
int it = 0, val = 1;
if (todo != -1){
it = todo, val = v[todo];
}
if (todo == -1) todo = 0;
do{
res[it] = val;
val++, it++;
it %= n;
val = (val - 1) % n + 1;
}while(it != todo);
vector<pii> td;
for (int i = 0; i < n; i++){
if (v[i] == 0){
td.pb({gondolaSeq[i], res[i]});
replacementSeq[gondolaSeq[i] - (n + 1)] = res[i];
}
}
if (td.empty()) return 0;
sort(td.begin(), td.end());
pii tmp = td.back();
int last = tmp.nd;
replacementSeq[tmp.st - (n + 1)] = 0;
for (int i = n + 1; i <= tmp.st; i++){
if (replacementSeq[i - (n + 1)] == 0){
replacementSeq[i - (n + 1)] = last;
last = i;
}
}
return tmp.st - n;
}
//----------------------
int mul(ll a, ll b){
return (a * b) % modulo;
}
int add(ll a, ll b){
if (a + b < modulo) return a + b;
return a + b - modulo;
}
int fe(ll a, ll b){
if (b == 0) return 1;
if (b % 2) return mul(a, fe(a, b - 1));
ll tmp = fe(a, b / 2);
return mul(tmp, tmp);
}
int countReplacement(int n, int inputSeq[])
{
set<int> s;
vector<int> v(n, 0);
for (int i = 0; i < n; i++){
int curr = inputSeq[i];
if (curr <= n) v[i] = curr;
s.insert(curr);
}
if (s.size() < n) return 0;
int todo = -1;
for (int i = 0; i < n; i++)
if (v[i] != 0) todo = i;
vector<int> res(n, 0);
int it = 0, val = 1;
int flag = 0;
if (todo != -1){
it = todo, val = v[todo];
}
if (todo == -1) flag = 1, todo = 0;
do{
res[it] = val;
val++, it++;
it %= n;
val = (val - 1) % n + 1;
}while(it != todo);
for (int i = 0; i < n; i++){
if (v[i] != 0 && v[i] != res[i]) return 0;
}
vector<int> td;
for (int i = 0; i < n; i++){
if (v[i] == 0){
td.pb(inputSeq[i]);
}
}
if (td.empty()) return 1;
int ans = 1;
sort(td.begin(), td.end());
int lst = n;
int m = td.size();
for (int i = 0; i < m; i++){
ans = mul(ans, fe(m - i, td[i] - lst - 1));
lst = td[i];
}
if (flag) ans = mul(ans, n);
return ans;
}
/*
int gondolaSequence[100001];
int replacementSequence[250001];
int main()
{
fileio();
int i, n, tag;
int nr;
assert(scanf("%d", &tag)==1);
assert(scanf("%d", &n)==1);
for(i=0;i< n;i++)
assert( scanf("%d", &gondolaSequence[i]) ==1);
switch (tag){
case 1: case 2: case 3:
printf("%d\n", valid(n, gondolaSequence));
break;
case 4: case 5: case 6:
nr = replacement(n, gondolaSequence, replacementSequence);
printf("%d ", nr);
if (nr > 0)
{
for (i=0; i<nr-1; i++)
printf("%d ", replacementSequence[i]);
printf("%d\n", replacementSequence[nr-1]);
}
else printf("\n");
break;
case 7: case 8: case 9: case 10:
printf("%d\n", countReplacement(n, gondolaSequence));
break;
}
return 0;
}
*/
