#include <bits/stdc++.h>
#include "gondola.h"
using namespace std;
const int md = (int) 1e9 + 9;
inline int mul(int x, int y) {
return (int) ((long long) x * y % md);
}
inline int power(int x, int y) {
int res = 1;
while (y) {
if (y & 1) {
res = mul(res, x);
}
x = mul(x, x);
y >>= 1;
}
return res;
}
int valid(int n, int inputSeq[]) {
vector<int> a(inputSeq, inputSeq + n);
sort(a.begin(), a.end());
if (unique(a.begin(), a.end()) != a.end()) {
return 0;
}
int p = min_element(inputSeq, inputSeq + n) - inputSeq;
for (int i = 0; i < n; ++i) {
if (inputSeq[(p + i) % n] <= n && inputSeq[(p + i) % n] != inputSeq[p] + i) {
return 0;
}
}
return 1;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[]) {
int q = min_element(gondolaSeq, gondolaSeq + n) - gondolaSeq;
if (gondolaSeq[q] <= n) {
q = (q - (gondolaSeq[q] - 1) + n) % n;
}
int p = max_element(gondolaSeq, gondolaSeq + n) - gondolaSeq;
int m = gondolaSeq[p];
vector<int> pos(m + 1, -1);
for (int i = 0; i < n; ++i) {
pos[gondolaSeq[i]] = (i - q + n) % n + 1;
}
for (int i = n + 1; i <= m; ++i) {
if (pos[i] != -1) {
replacementSeq[i - n - 1] = pos[i];
} else {
replacementSeq[i - n - 1] = pos[m];
pos[m] = i;
}
}
return m - n;
}
int countReplacement(int n, int inputSeq[]) {
if (!valid(n, inputSeq)) {
return 0;
}
sort(inputSeq, inputSeq + n);
int ans = 1;
if (inputSeq[0] > n) {
ans = n;
}
for (int i = 0; i < n; ++i) {
if (inputSeq[i] > n) {
ans = mul(ans, power(n - i, inputSeq[i] - max(n, i ? inputSeq[i - 1] : n) - 1));
}
}
return ans;
}
