#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
#define mod 1000000009
#define h1 7897897897897897
#define h2 7897466719774591
#define b1 98762051
#define b2 98765431
#define inf 1000000000
#define pi 3.1415926535897932384626
#define LMAX 9223372036854775807
#define ll long long
#define fi first
#define se second
#define pii pair<int, int>
#define pll pair<ll, ll>
#define vi vector<int>
#define vl vector<ll>
#define vp vector<pii>
#define SET(a, b) memset(a, b, sizeof(a))
#define all(x) (x).begin(), (x).end()
#define FOR(i, a, b) for (int i = (a); i <= (b); i++)
#define FORD(i, a, b) for (int i = (a); i >= (b); i--)
int f[250005], ans[250005], required[250005];
int valid(int n, int a[])
{
FOR(i, 0, n-1) {
f[a[i]]++;
if (f[a[i]] == 2) return 0;
}
int st = -1;
FOR(i, 0, n-1) {
if (a[i] <= n) {
st = i;
break;
}
}
if (st == -1) return 1;
int i = st, cur = a[i];
do {
if (a[i] == cur || a[i] > n) {}
else return 0;
cur++;
if (cur > n) cur = 1;
i++;
if (i == n) i = 0;
} while (i != st);
return 1;
}
//----------------------
int replacement(int n, int a[], int replace[])
{
int st = -1;
FOR(i, 0, n-1) {
if (a[i] <= n) {
st = i;
break;
}
}
set <int> s;
int maxx = 0;
SET(required, -1);
FOR(i, 0, n-1) {
required[a[i]] = i;
maxx = max(maxx, a[i]);
if (a[i] > n) s.insert(i);
}
if (st == -1) {
FOR(i, 0, n-1) f[i] = i+1;
} else {
int i = st, cur = a[i];
do {
f[i] = cur;
cur++;
if (cur > n) cur = 1;
i++;
if (i == n) i = 0;
} while (i != st);
}
FOR(i, n+1, maxx) {
if (required[i] != -1) {
replace[i-n-1] = f[required[i]];
cerr<<replace[i-n-1]<<endl;
s.erase(required[i]);
f[required[i]] = i;
} else {
int pos = *s.begin();
replace[i-n-1] = f[pos];
if (i == a[pos]) s.erase(s.begin());
f[pos] = i;
}
}
return maxx - n;
}
//----------------------
int countReplacement(int n, int a[])
{
ll ans = 1;
if (!valid(n, a)) return 0;
int st = -1;
FOR(i, 0, n-1) {
if (a[i] <= n) {
st = i;
break;
}
}
set <int> s;
int maxx = 0;
SET(required, -1);
FOR(i, 0, n-1) {
required[a[i]] = i;
maxx = max(maxx, a[i]);
if (a[i] > n) s.insert(i);
}
ll sz = s.size();
FOR(i, n+1, maxx) {
if (required[i] != -1) {
s.erase(required[i]);
sz--;
} else {
ans = ans * sz % mod;
}
}
return ans;
}
