#include <iostream>
#include <algorithm>
#include <vector>
#include "gondola.h"
#define MAX 250000
#define MOD 1000000009
using namespace std;
int mark[MAX + 10];
vector <pair <int, int>> v;
int valid(int n, int inputSeq[])
{
int posOrig = -1;
for (int i = 0; i < n; i++)
{
if (mark[inputSeq[i]] == 1)
return 0;
if (inputSeq[i] <= n)
posOrig = i;
mark[inputSeq[i]] = 1;
}
if (posOrig == -1)
return 1;
int pos = posOrig;
for (int i = 1; i <= n; i++)
{
if (inputSeq[pos] <= n && (inputSeq[pos] - inputSeq[posOrig] + n) % n != (pos - posOrig + n) % n)
return 0;
pos = (pos + 1) % n;
}
return 1;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int posOrig = -1;
for (int i = 0; i < n; i++)
if (gondolaSeq[i] <= n)
posOrig = i;
if (posOrig == -1)
for (int i = 0; i < n; i++)
v.push_back({gondolaSeq[i], i + 1});
else
{
int pos = posOrig;
int g = gondolaSeq[posOrig];
for (int i = 1; i <= n; i++)
{
if (gondolaSeq[pos] > n)
v.push_back({gondolaSeq[pos], g});
pos = (pos + 1) % n;
if (g == n - 1)
g = n;
else
g = (g + 1) % n;
}
}
sort(v.begin(), v.end());
int l = 0, nn = n + 1;
for (auto it : v)
{
replacementSeq[l] = it.second;
l++;
nn++;
while (nn <= it.first)
{
replacementSeq[l] = nn - 1;
l++;
nn++;
}
}
return l;
}
int fastPow(int base, int exp)
{
int ans = 1;
while (exp != 0)
if (exp % 2 == 0)
{
exp = exp / 2;
base = 1LL * base * base % MOD;
}
else
{
exp--;
ans = 1LL * ans * base % MOD;
}
return ans;
}
int countReplacement(int n, int inputSeq[])
{
if (valid(n, inputSeq) == 0)
return 0;
int posOrig = -1;
for (int i = 0; i < n; i++)
if (inputSeq[i] <= n)
posOrig = i;
int ans;
if (posOrig == -1)
{
ans = n;
for (int i = 0; i < n; i++)
v.push_back({inputSeq[i], i + 1});
}
else
{
ans = 1;
int pos = posOrig;
int g = inputSeq[posOrig];
for (int i = 1; i <= n; i++)
{
if (inputSeq[pos] > n)
v.push_back({inputSeq[pos], g});
pos = (pos + 1) % n;
if (g == n - 1)
g = n;
else
g = (g + 1) % n;
}
}
sort(v.begin(), v.end());
int cntGreater = v.size(), aux = n;
for (auto it : v)
{
ans = 1LL * ans * fastPow(cntGreater, it.first - aux - 1) % MOD;
cntGreater--;
aux = it.first;
}
return ans;
}
