#include <iostream>
#include <vector>
#include "gondola.h"
using namespace std;
using ll = long long;
int valid(int n, int g[]) {
int p = 0;
for (int i = 0; i < n; i++) if (g[i] <= n) p = (g[i] - i + n) % n;
for (int i = 0; i < n; i++) if (g[i] <= n && (g[i] - i + n) % n != p) return 0;
return 1;
}
int replacement(int n, int g[], int r[]) {
int p = 0, cnt = 0, mx = 0;
vector <int> rev(1e6 + 1, -1);
vector <int> cur(n, 0);
for (int i = 0; i < n; i++) {
if (g[i] <= n) { p = (g[i] - i + n) % n; cnt++; }
mx = max(mx, g[i]);
rev[g[i]] = i;
}
for (int i = 0; i < n; i++) cur[i] = (i + p) % n;
cur[n - p] = n;
for (int i = n + 1; i <= mx; i++) {
if (rev[i] == -1) r[i - n - 1] = cur[rev[mx]];
else r[i - n - 1] = cur[rev[i]];
}
return mx - n;
}
int countReplacement(int n, int g[]) {
if (!valid(n, g)) return 0;
int cnt = 0, mx = 0;
ll ans = 1, MOD = 1e9 + 9;
vector <int> rev(1e6 + 1, -1);
for (int i = 0; i < n; i++) {
if (g[i] <= n) cnt++;
mx = max(mx, g[i]);
rev[g[i]] = i;
}
for (int i = n + 1; i <= mx; i++) {
if (rev[i] == -1) { ans *= (n - cnt); ans %= MOD; }
else cnt++;
}
return ans;
}
