#include "gondola.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace std;
using namespace __gnu_pbds;
#ifdef _WIN32
#define getchar_unlocked _getchar_nolock
#endif
#define mp make_pair
#define mt make_tuple
#define pb push_back
#define pf push_front
#define ppb pop_back
#define ppf pop_front
#define eb emplace_back
#define g0(a) get<0>(a)
#define g1(a) get<1>(a)
#define g2(a) get<2>(a)
#define g3(a) get<3>(a)
mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());
typedef double db;
typedef long long ll;
typedef long double ld;
typedef pair<int, int> ii;
typedef tuple<int, int, int> iii;
typedef tuple<int, int, int, int> iiii;
typedef tree<ii, null_type, less<ii>, rb_tree_tag, tree_order_statistics_node_update> ordered_set;
int valid(int n, int inputSeq[]) {
int pos = -1;
vector<int> S;
for (int i = 0; i < n; i++)
if (inputSeq[i] <= n) {
pos = i;
break;
}
for (int i = 0; i < n; i++)
if (inputSeq[i] > n)
S.pb(inputSeq[i]);
sort(S.begin(), S.end());
if (unique(S.begin(), S.end()) != S.end()) return 0;
if (pos == -1) return 1;
int curr = inputSeq[pos];
for (int i = pos; i < n; i++) {
if (inputSeq[i] <= n && curr != inputSeq[i]) return 0;
curr++;
if (curr == n + 1) curr = 1;
}
for (int i = 0; i < pos; i++) {
if (inputSeq[i] <= n && curr != inputSeq[i]) return 0;
curr++;
if (curr == n + 1) curr = 1;
}
return 1;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[]) {
int pos = -1, l = 0;
for (int i = 0; i < n; i++)
if (gondolaSeq[i] <= n) {
pos = i;
break;
}
int curr = (pos == -1 ? 1 : gondolaSeq[pos]);
if (pos == -1) pos = 0;
vector<iii> need;
for (int i = pos; i < n; i++) {
if (gondolaSeq[i] > n) need.eb(gondolaSeq[i], curr, i);
curr++;
if (curr == n + 1) curr = 1;
}
for (int i = 0; i < pos; i++) {
if (gondolaSeq[i] > n) need.eb(gondolaSeq[i], curr, i);
curr++;
if (curr == n + 1) curr = 1;
}
sort(need.begin(), need.end());
int prv = -1;
for (auto i : need) {
int iter = 0;
for (int j = max(prv, n); j < g0(i); j++) {
replacementSeq[l] = (iter ? l + n : g1(i));
l++;
iter++;
}
prv = g0(i);
}
return l;
}
const int MOD = 1e9 + 9;
int exp_mod(int a, int b) {
int r = 1;
while (b) {
if (b & 1) r = (ll)r * (ll)a % MOD;
a = (ll)a * (ll)a % MOD;
b >>= 1;
}
return r;
}
int countReplacement(int n, int inputSeq[]) {
if (!valid(n, inputSeq)) return 0;
int pos = -1, ans = 1;
for (int i = 0; i < n; i++)
if (inputSeq[i] <= n) {
pos = i;
break;
}
vector<int> need;
for (int i = 0; i < n; i++)
if (inputSeq[i] > n) need.pb(inputSeq[i]);
sort(need.begin(), need.end());
int prv = -1, lft = need.size();
for (auto i : need) {
ans = (ll)ans * (ll)exp_mod(lft, i - max(prv, n) - 1) % MOD;
prv = i;
lft--;
}
if (pos == -1) ans = (ll)ans * (ll)n % MOD;
return ans;
}
