#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#pragma GCC optimize("trapv")
int valid(int n, int inputSeq[])
{
set<int> st;
int cur = -1;
for(int i = 0; i < n; i++){
int x = inputSeq[i];
if(st.find(x) != st.end())return 0;
st.insert(x);
if(cur == -1 && x <= n){
cur = x+1;
if(cur > n)cur = 1;
}else if(cur != -1){
if(x <= n && x != cur) return 0;
cur++;
if(cur > n)cur = 1;
}
}
return 1;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
vector< pair<int,int> > v;
int cur = -1, st = -1;
for(int i = 0; i < n; i++){
int x = gondolaSeq[i];
if(cur == -1 && x <= n){
st = i;
cur = x+1;
if(cur > n)cur = 1;
}else if(cur != -1){
if(x > n)v.push_back({x,cur});
cur++;
if(cur > n)cur = 1;
}
}
if(cur == -1){
st = n;
cur = 1;
}
for(int i = 0; i < st; i++){
int x = gondolaSeq[i];
if(x > n)v.push_back({x,cur});
cur++;
if(cur > n)cur = 1;
}
sort(v.begin(),v.end());
int nxt = n+1, tam = 0;
for(int i = 0; i < v.size(); i++){
int og = v[i].second, fim = v[i].first;
replacementSeq[tam] = og; tam++;
nxt++;
while(nxt-1 < fim){
replacementSeq[tam] = nxt-1; tam++;
nxt++;
}
}
return tam;
}
//----------------------
long long MOD = 1000000009;
long long expo(long long a, long long b){
if(b == 0)return 1;
long long x = expo(a,b/2);
x = (x*x)%MOD;
if(b%2 == 1)return (x*a)%MOD;
return x;
}
int countReplacement(int n, int inputSeq[])
{
if(valid(n,inputSeq) == 0)return 0;
vector< int > v;
for(int i = 0; i < n; i++)
if(inputSeq[i] > n)v.push_back(inputSeq[i]);
sort(v.begin(),v.end());
if(v.size() == 0)return 1;
long long ans = 1, last = n+1, qtd = v.size();
for(int i = 0; i < v.size(); i++){
ans = (expo(qtd,v[i]-last) * ans)%MOD;
qtd--; last = v[i]+1;
}
if(v.size() == n)ans = (ans*n)%MOD;
return ans;
}
