#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define pb push_back
int valid(int n, int inputSeq[])
{
bool flag=1;
int req=-1;
for(int i=0;i<n;i++){
if(req==-1 && inputSeq[i]<=n)req=inputSeq[i]+1;
else if(inputSeq[i]<=n && req!=inputSeq[i])flag=0;
else if(req!=-1)req++;
if(req>n)req=1;
}
sort(inputSeq,inputSeq+n);
for(int i=1;i<n;i++){
if(inputSeq[i]==inputSeq[i-1])return 0;
}
return flag;
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int og[n],crnt=n+1,idx=0;
vector<pair<int,int>> vec;
for(int i=0;i<n;i++){
og[i]=i+1;
if(gondolaSeq[i]<=n){
og[i]=gondolaSeq[i];
for(int j=i+1;j<n;j++){
og[j]=og[j-1]+1;
if(og[j]>n)og[j]=1;
}
if(i>0)og[0]=og[n-1]+1;
if(og[0]>n)og[0]=1;
for(int j=1;j<i;j++){
og[j]=og[j-1]+1;
if(og[j]>n)og[j]=1;
}
break;
}
}
for(int i=0;i<n;i++)vec.pb({gondolaSeq[i],og[i]});
sort(vec.begin(),vec.end());
for(int i=0;i<n;i++){
while(vec[i].first>=crnt){
replacementSeq[idx++]=vec[i].second;
vec[i].second=crnt;
crnt++;
}
}
return idx;
}
//----------------------
long long MOD=1e9+7;
long long fast_pow(long long base,long long p,long long rem=1){
if(p==0)return 1;
base%=MOD; rem%=MOD;
if(p==1)return base*rem%MOD;
if(p%2)return fast_pow(base*base,p/2,rem*base);
return fast_pow(base*base,p/2,rem);
}
int countReplacement(int n, int inputSeq[])
{
if(!valid(n,inputSeq))return 0;
sort(inputSeq,inputSeq+n);
long long ans=1,crnt=n+1;
bool flag=1;
for(int i=0;i<n;i++){
if(inputSeq[i]<=n)flag=0;
if(inputSeq[i]>=crnt){
ans*=fast_pow(n-i,inputSeq[i]-crnt);
crnt=inputSeq[i]+1;
}
ans%=MOD;
}
if(flag)ans*=n;
return ans;
}
