#include "gondola.h"
#include <bits/stdc++.h>
#define pb push_back
#define all(x) x.begin(), x.end()
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;
typedef vector<int> vi;
typedef vector<ll> vl;
typedef vector<pii> vpi;
typedef vector<pll> vpl;
const int MAXN = 1e6 + 5;
vi input;
unordered_map<int, int> vis;
int valid(int N, int inputSeq[])
{
input.clear();
for(int i = 0; i < N; i++)
input.pb(inputSeq[i]);
int ans = 0, one = 0;
vis.clear();
for(int i = 0; i < N; i++)
{
if(vis[input[i]])
return 0;
vis[input[i]]++;
}
for(int i = 0; i < N; i++)
{
if(input[i] <= N)
{
one = 1;
int idx;
for(int j = 0; j < N; j++)
{
idx = (i + (j + 1 - input[i]) + N) % N;
if(input[idx] == j + 1 || input[idx] > N)
ans++;
}
cerr << i << " " << input[i] << " " << ans << "\n";
break;
}
}
if(!one)
return 1;
return (ans == N);
}
int replacement(int N, int gondolaSeq[], int replacementSeq[])
{
input.clear();
for(int i = 0; i < N; i++)
input.pb(gondolaSeq[i]);
int one = 0;
for(int i = 0; i < N; i++)
if(input[i] <= N)
one = (i - input[i] + 1 + N) % N;
vpi seq;
for(int i = 0; i < N; i++)
seq.pb({input[(one + i) % N], i + 1});
sort(all(seq));
int curr = 0, newGondola = N + 1;
for(int i = 0; i < N; i++)
{
while(seq[i].second != seq[i].first)
{
replacementSeq[curr++] = seq[i].second;
seq[i].second = newGondola++;
}
}
return curr;
}
const ll MOD = 1e9 + 9;
ll binexp(ll b, ll e)
{
if(e == 0) return 1;
if(e&1) return (b * binexp(b, e-1)) % MOD;
else
{
ll aux = binexp(b, e/2);
return (aux*aux) % MOD;
}
}
int countReplacement(int N, int inputSeq[])
{
if(!valid(N, inputSeq))
return 0;
cerr << "valid\n";
int one = -1;
for(int i = 0; i < N; i++)
if(input[i] <= N)
one = (i - input[i] + 1 + N) % N;
vpi seq;
for(int i = 0; i < N; i++)
seq.pb({input[(max(one, 0) + i) % N], i + 1});
sort(all(seq));
int last = N;
ll ans = 1;
for(int i = 0; i < N; i++)
{
if(seq[i].first <= N)
continue;
cerr << seq[i].first << " " << last << "\n";
ans *= binexp(N - i, seq[i].first - last - 1);
cerr << ans << "\n";
last = seq[i].first;
ans %= MOD;
}
if(one < 0)
ans = (ans * N) % MOD;
return ans;
}
