#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const ll mod = 1000000009;
ll mpow(ll b, ll e) {
if (e == 0) return 1;
if (e & 1) return mpow(b, e - 1) * b % mod;
return mpow(b * b % mod, e >> 1);
}
vector<int> arr(int *s, int n, int d = 0) {
vector<int> v(s, s + n);
for (int i = 0; i < n; i++) v[i] += d;
return v;
}
int rotatoize(vector<int>& v) {
int p = 0, n = v.size();
while (p < n && v[p] >= n) p++;
if (p < n) rotate(v.begin(), v.begin() + (p - v[p] + n) % n, v.end());
return p;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[]) {
vector<int> gon = arr(gondolaSeq, n, -1);
vector<int> rep;
int p = rotatoize(gon);
vector<int> inds(n), curr(n);
iota(curr.begin(), curr.end(), 0);
iota(inds.begin(), inds.end(), 0);
sort(inds.begin(), inds.end(), [&](int i, int j) { return gon[i] < gon[j]; });
int spare = n;
for (int i : inds) {
while (spare <= gon[i]) {
rep.push_back(curr[i]);
curr[i] = spare++;
}
}
for (int i = 0; i < rep.size(); i++) replacementSeq[i] = rep[i] + 1;
return rep.size();
}
int countReplacement(int n, int inputSeq[]) {
vector<int> gon = arr(inputSeq, n, -1);
int p = rotatoize(gon);
int blanks = 0;
for (int i = 0; i < n; i++) {
if (gon[i] < n) {
if (gon[i] != i) return 0;
} else blanks++;
}
vector<int> vals = gon;
sort(vals.begin(), vals.end());
ll ans = blanks == n ? n : 1;
vector<int> inds(n);
iota(inds.begin(), inds.end(), 0);
sort(inds.begin(), inds.end(), [&](int i, int j) { return gon[i] < gon[j]; });
int spare = n, prev = -1;
for (int i : inds) {
if (prev == gon[i]) return 0;
prev = gon[i];
if (spare <= gon[i]) {
ans = ans * mpow(blanks--, max(0, gon[i] - spare)) % mod;
spare = gon[i] + 1;
}
}
assert(blanks == 0);
return int(ans);
}
int valid(int n, int inputSeq[]) {
return countReplacement(n, inputSeq) != 0;
}
