#include "gondola.h"
#include <bits/stdc++.h>
#define ll long long
using namespace std;
int valid(int n, int g[]) {
int idx = -1;
map <int, bool> vis;
for (int i = 0;i < n;i++) {
if (vis[g[i]] == true) return 0;
vis[g[i]] = true;
if (g[i] <= n && idx == -1) {
idx = i;
}
}
if (idx == -1) return 1;
int cnt = g[idx];
for (int i = idx + 1;;i++) {
i %= n;
if (i == idx) break;
cnt %= n;
cnt++;
if (g[i] <= n && g[i] != cnt) return 0;
}
return 1;
}
//----------------------
int replacement(int n, int g[], int r[]) {
int idx = -1;
map <int, bool> vis;
int mx = 0;
for (int i = 0;i < n;i++) {
if (vis[g[i]] == true) return 0;
vis[g[i]] = true;
if (g[i] <= n && idx == -1) {
idx = i;
}
mx = max(mx, g[i]);
}
int sz = 0;
int exp[n] = {0};
if (idx == -1) {
exp[0] = 1;
int cnt = 1;
for (int i = 1;;i++) {
i %= n;
if (i == 0) break;
cnt %= n;
cnt++;
exp[i] = cnt;
}
}
else {
exp[idx] = g[idx];
int cnt = g[idx];
for (int i = idx + 1;;i++) {
i %= n;
if (i == idx) break;
cnt %= n;
cnt++;
exp[i] = cnt;
}
}
// for (int i = 0;i < n;i++) {
// cout << exp[i] << ' ';
// }
// cout << endl;
vector <pair <int, int>> upd;
for (int i = 0;i < n;i++) {
if (exp[i] != g[i]) {
upd.push_back({g[i], exp[i]});
}
}
sort(upd.begin(), upd.end());
for (auto [x, y] : upd) {
r[sz] = y;
sz++;
for (int i = n + sz;i < x;i++) {
r[sz] = i;
sz++;
}
}
return mx - n;
}
const int mod = 1e9 + 9;
int poww(int x, int y) {
ll res = 1;
x = x % mod;
while (y > 0) {
if (y % 2 == 1) {
res = 1LL * res * x % mod;
}
x = 1LL * x * x % mod;
y /= 2;
}
res = 1LL * res * x % mod;
return res;
}
int countReplacement(int n, int g[]) {
if (!valid(n, g)) {
return 0;
}
ll mult = n;
vector <ll> saves;
for (int i = 0;i < n;i++) {
if (g[i] > n) {
saves.push_back(g[i]);
}
if (g[i] <= n) {
mult = 1;
}
}
sort(saves.begin(), saves.end());
ll curr = n;
int sz = saves.size();
ll res = 1;
for (int i = 0;i < saves.size();i++) {
int iter = saves[i] - curr - 1;
if (iter == 0) {
sz--;
curr = saves[i];
continue;
}
res = (res * poww(sz, iter)) % mod;
sz--;
curr = saves[i];
}
return (res * mult) % mod;
}
