#include "gondola.h"
#include <vector>
#include <algorithm>
#include <iostream>
#define int int64_t
using namespace std;
const int mod = 1e9 + 9;
signed fastpowmod(int base, int exp)
{
int res = 1;
for (; exp; exp /= 2)
{
if (exp & 1) res = (res*base) % mod;
base = (base*base) % mod;
}
return res;
}
signed valid(signed n, signed inputSeq[])
{
vector<int> dcheck;
for (int i = 0; i < n; i++)
{
inputSeq[i]--;
dcheck.push_back(inputSeq[i]);
}
sort(dcheck.begin(), dcheck.end());
for (int i = 1; i < n; i++)
{
if (dcheck[i] == dcheck[i - 1]) return 0;
}
int zval = 0;
for (int i = 0; i < n; i++)
{
if (inputSeq[i] < n)
{
zval = inputSeq[i] - i;
break;
}
}
for (int i = 0; i < n; i++)
{
if (inputSeq[i] < n)
{
if ((zval + i + n) % n != inputSeq[i]) return 0;
}
}
return 1;
}
//----------------------
signed replacement(signed n, signed gondolaSeq[], signed replacementSeq[])
{
vector<int> Seq;
for (int i = 0; i < n; i++) Seq.push_back(gondolaSeq[i] - 1);
int zval = 0;
for (int i = 0; i < n; i++)
{
if (Seq[i] < n)
{
zval = Seq[i] - i;
break;
}
}
rotate(Seq.rbegin(), Seq.rbegin() + ((zval + n) % n), Seq.rend());
int mmax = *max_element(Seq.begin(), Seq.end());
int mind = -1;
for (int i = 0; i <= mmax - n; i++) replacementSeq[i] = -1;
for (int i = 0; i < n; i++)
{
if (Seq[i] == mmax) mind = i;
if (Seq[i] >= n) replacementSeq[Seq[i] - n] = i + 1;
}
mind++;
for (int i = 0; i <= mmax - n; i++)
{
if (replacementSeq[i] == -1)
{
replacementSeq[i] = mind;
mind = n + i + 1;
}
}
replacementSeq[mmax - n] = mind;
return mmax - n + 1;
}
//----------------------
signed countReplacement(signed n, signed inputSeq[])
{
if (!valid(n, inputSeq)) return 0;
vector<int> ndef;
int res = n;
int nused = 0;
for (int i = 0; i < n; i++)
{
if (inputSeq[i] < n) { res = 1; nused++; }
else
{
ndef.push_back(inputSeq[i]);
}
}
sort(ndef.begin(), ndef.end());
int curr = n;
for (int i = 0; i < (int)ndef.size(); i++)
{
res = (res * fastpowmod(n - nused - i, ndef[i] - curr)) % mod;
curr = ndef[i] + 1;
}
return res;
}
