#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
int valid(int n, int inputSeq[]) {
vector<int> v(2 * n);
for (int i = 0; i < 2 * n; ++ i)
v[i] = inputSeq[i % n];
sort(inputSeq, inputSeq + n);
for (int i = 1; i < n; ++ i) {
if (inputSeq[i] == inputSeq[i - 1])
return 0;
}
if (inputSeq[0] > n)
return 1;
int ind = 0;
while (ind < n && v[ind] != inputSeq[0])
++ ind;
for (int i = 0; i < n; ++ i) {
if (v[ind + i] <= n && v[ind + i] != inputSeq[0] + i)
return 0;
}
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int mn = 0;
for (int i = 0; i < n; ++ i) {
if (gondolaSeq[i] < gondolaSeq[mn])
mn = i;
}
vector<pair<int, int>> ord;
vector<int> v(2 * n);
v.resize(2 * n);
for (int i = 0; i < 2 * n; ++ i)
v[i] = gondolaSeq[i % n];
int l = 0;
for (int i = mn; i < mn + n; ++ i) {
if (v[i] > n) {
ord.push_back({v[i], i - mn + v[mn]});
}
}
ord.push_back({n, -1});
sort(ord.begin(), ord.end());
for (int i = 1; i < (int)ord.size(); ++ i) {
int val = ord[i].second;
for (int j = ord[i - 1].first + 1; j <= ord[i].first; ++ j) {
replacementSeq[l ++] = val;
val = j;
}
}
return l;
}
//----------------------
static const int mod = 1e9 + 9;
long long lgput (long long b, int p) {
long long sol = 1;
while (p > 0) {
if (p & 1)
sol = sol * b % mod;
b = b * b % mod;
p >>= 1;
}
return sol;
}
int countReplacement(int n, int inputSeq[])
{
if (valid(n, inputSeq) == 0)
return 0;
long long ans = 1;
int mn = 0;
for (int i = 0; i < n; ++ i) {
if (inputSeq[i] < inputSeq[mn])
mn = i;
}
vector<int> v(2 * n);
v.resize(2 * n);
for (int i = 0; i < 2 * n; ++ i)
v[i] = inputSeq[i % n];
vector<int> ord;
for (int i = mn; i < mn + n; ++ i) {
if (v[i] > n) {
ord.push_back(v[i]);
}
}
ord.push_back(n);
sort(ord.begin(), ord.end());
for (int i = 1; i < (int)ord.size(); ++ i) {
int cnt = ord[i] - 1 - ord[i - 1];
ans = ans * lgput((int)ord.size() - i, cnt) % mod;
}
return ans;
}
