#include "gondola.h"
#include <bits/stdc++.h>
#pragma GCC Optimize("O3")
#define FOR(i, x, y) for (int i = x; i < y; i++)
#define MOD 1000000009
typedef long long ll;
using namespace std;
int valid(int n, int inputSeq[]) {
vector<int> gondolas;
FOR(i, 0, n) gondolas.push_back(inputSeq[i]);
sort(gondolas.begin(), gondolas.end());
FOR(i, 1, n) if (gondolas[i] == gondolas[i - 1]) return 0;
FOR(i, 0, n) {
if (inputSeq[i] <= n) {
FOR(j, 1, n + 1) {
int k = (i + j - inputSeq[i]) % n;
while (k < 0) k += n;
if (inputSeq[k] <= n && inputSeq[k] != j) return 0;
}
return 1;
}
}
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[]) {
vector<pair<int, int>> broken;
int offset = 0;
FOR(i, 0, n) {
if (gondolaSeq[i] > n)
broken.push_back({gondolaSeq[i], i + 1});
else
offset = i - gondolaSeq[i] + 1;
}
FOR(i, 0, broken.size()) {
broken[i].second = (broken[i].second - offset - 1 + n) % n + 1;
}
int indx = 0, curr = n;
sort(broken.begin(), broken.end());
for (pair<int, int> i : broken) {
replacementSeq[indx++] = i.second;
curr++;
FOR(j, curr, i.first)
replacementSeq[indx++] = j;
curr = i.first;
}
return indx;
}
//----------------------
ll expo(ll x, ll y) {
ll res = 1;
x = x % MOD;
while (y > 0) {
if (y & 1) res = (res * x) % MOD;
y = y >> 1;
x = (x * x) % MOD;
}
return res;
}
int countReplacement(int n, int inputSeq[]) {
if (!valid(n, inputSeq)) return 0;
// If there are k replaced cars {a, b}, {c, d}, ...
// Then ans is k^(d - b) * (k - 1)^(f - d) + ...
vector<ll> broken;
broken.push_back(0);
FOR(i, 0, n) {
if (inputSeq[i] > n)
broken.push_back((ll) (inputSeq[i] - n));
}
sort(broken.begin(), broken.end());
ll ans = 1;
FOR(i, 1, broken.size()) {
ans = (ans * expo(ll(broken.size() - i), (ll)(broken[i] - broken[i - 1] - 1))) % MOD;
}
if (broken.size() == n + 1) ans = (ans * (ll)(n)) % MOD;
return ans;
}
// int gondolas[100000], replacements[100000];
// int main() {
// int T, n;
// cin >> T >> n;
// FOR(i, 0, n) cin >> gondolas[i];
// if (T < 4) cout << valid(n, gondolas);
// else if (T < 7) {
// int k = replacement(n, gondolas, replacements);
// cout << k << ' ';
// FOR(i, 0, k) cout << replacements[i] << ' ';
// }
// else cout << countReplacement(n, gondolas);
// }
