#include "gondola.h"
#include<bits/stdc++.h>
using namespace std ;
const long long mod = 1e9 + 7 ;
long long power(long long a , long long p)
{
long long ret = 1 ;
while(p)
{
if(p&1) ret = (ret*a)%mod ;
a = (a*a)%mod ;
p >>= 1 ;
}
return ret ;
}
int valid(int n, int inputSeq[])
{
int idx = -1 , cur = 0 ;
map<int,int> vis ;
for(int i = 0 ; i < n ; ++i)
{
if(vis.find(inputSeq[i])!=vis.end()) return 0 ;
vis[inputSeq[i]] = 1 ;
}
for(int i = 0 ; i < n ; ++i)
{
if(inputSeq[i]<=n)
{
idx = i ;
cur = inputSeq[i] - 1 ;
break ;
}
}
if(idx<0) return 1 ;
for(int i = idx ; i < n ; ++i)
{
if((inputSeq[i]<=n) && (inputSeq[i]!=(cur+1))) return 0 ;
cur = (cur+1)%n ;
}
return 1 ;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
vector<pair<int,int> > v ;
vector<int> ans ;
int cur = 0 , idx = 0 ;
for(int i = 0 ; i < n ; ++i)
{
if(gondolaSeq[i]<=n)
{
idx = i ;
cur = gondolaSeq[i] - 1 ;
break ;
}
}
for(int i = idx ; i < n ; ++i)
{
if(gondolaSeq[i]>n)
{
v.push_back({gondolaSeq[i],cur+1}) ;
}
cur = (cur+1)%n ;
}
for(int i = 0 ; i < idx ; ++i)
{
if(gondolaSeq[i]>n)
{
v.push_back({gondolaSeq[i],cur+1}) ;
}
cur = (cur+1)%n ;
}
sort(v.begin(),v.end()) ;
cur = n ;
for(pair<int,int> p : v)
{
ans.push_back(p.second) , ++cur ;
while(cur<p.first)
{
ans.push_back(cur) ;
++cur ;
}
}
int siz = ans.size() ;
for(int i = 0 ; i < siz ; ++i)
{
replacementSeq[i] = ans[i] ;
}
return siz ;
}
int countReplacement(int n, int inputSeq[])
{
long long ans = 1 , mul = n ;
if(!valid(n,inputSeq)) return 0 ;
long long a[n+2] = {0} , siz = 0 ;
for(int i = 0 ; i < n ; ++i)
{
if(inputSeq[i]<=n) mul = 1 ;
a[++siz] = inputSeq[i] ;
}
sort(a+1,a+siz+1) ;
a[0] = n ;
for(int i = 1 ; i <= siz ; ++i)
{
long long cur = power(siz-i+1,a[i]-a[i-1]-1) ;
ans = (ans*cur)%mod ;
}
return (ans*mul)%mod ;
}
