#include <bits/stdc++.h>
#include "gondola.h"
using namespace std;
int valid(int n, int a[]) {
int N = 0;
for (int i = 0; i < n; ++i) {
N = max(N, a[i]);
}
vector<bool> ap(N + 1);
int pos = 0;
for (int i = 0; i < n; ++i) {
if (ap[a[i]]) {
return 0;
}
ap[a[i]] = true;
if (a[i] < a[pos]) {
pos = i;
}
}
if (a[pos] > n) {
return 1;
}
int x = a[pos];
for (int rep = 0; rep < n; ++rep) {
if (a[pos] <= n && a[pos] != x) {
return 0;
}
x += 1;
if (x == n + 1) {
x = 1;
}
pos += 1;
if (pos == n) {
pos = 0;
}
}
return 1;
}
void maxSelf(int &x, int y) {
if (x < y) {
x = y;
}
}
int replacement(int n, int a[], int sol[]) {
vector<int> v(n);
iota(v.begin(), v.end(), 1);
for (int i = 0; i < n; ++i) {
if (a[i] <= n) {
int x = a[i];
for (int rep = 0; rep < n; ++rep) {
v[i] = x;
x += 1;
if (x == n + 1) {
x = 1;
}
i += 1;
if (i == n) {
i = 0;
}
}
break;
}
}
int N = 0;
for (int i = 0; i < n; ++i) {
maxSelf(N, a[i]);
}
vector<int> w(N + 1);
for (int i = 0; i < n; ++i) {
w[a[i]] = v[i];
}
int len = 0, x = n + 1;
for (int i = 1; i <= N; ++i) {
if (w[i]) {
while (w[i] < i) {
sol[len++] = w[i];
w[i] = x;
x += 1;
}
}
}
return len;
}
const int mod = 1e9 + 9;
void multSelf(int &x, const int &y) {
x = (int64_t)x * y % mod;
}
int Pow(int x, int n) {
int ans = 1;
while (n) {
if (n & 1) {
multSelf(ans, x);
}
multSelf(x, x);
n >>= 1;
}
return ans;
}
int countReplacement(int n, int a[]) {
if (!valid(n, a)) {
return 0;
}
vector<int> v{n};
for (int i = 0; i < n; ++i) {
if (a[i] > n) {
v.emplace_back(a[i]);
}
}
int ans = 1, m = v.size();
for (int i = 1; i < m; ++i) {
multSelf(ans, Pow(m - i, v[i] - v[i - 1] - 1));
}
if (m == n + 1) {
multSelf(ans, n);
}
return ans;
}
