#include "gondola.h"
#include<bits/stdc++.h>
#define fi first
#define se second
#define pii pair<int,int>
#define mp make_pair
using namespace std;
const int mod=1e9+7;
const int N=1e5+5;
int ST[4*N],lazy[4*N];
void dolazy(int id,int l,int r)
{
if(lazy[id]==0) return ;
ST[id]+=lazy[id];
if(l!=r)
{
lazy[id*2]+=lazy[id];
lazy[id*2+1]+=lazy[id];
}
lazy[id]=0;
}
void update(int id,int l,int r,int u,int v,int val)
{
dolazy(id,l,r);
if(v<l||u>r) return ;
if(u<=l&&r<=v)
{
ST[id]+=val;
if(l!=r)
{
lazy[id*2]+=val;
lazy[id*2+1]+=val;
}
return ;
}
int mid=(l+r)/2;
update(id*2,l,mid,u,v,val);
update(id*2+1,mid+1,r,u,v,val);
ST[id]=min(ST[id*2],ST[id*2+1]);
}
int Power(int x,int n)
{
if(!n) return 1;
if(n%2) return 1ll*Power(x,n-1)*x%mod;
int tmp=Power(x,n/2);
return 1ll*tmp*tmp%mod;
}
int expect[N*2],initSeq[N];
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int offs = 0;
int dummy = 0;
int mx = -1;
memset(expect, -1, sizeof(expect));
for(int i = 0; i < n; i++){
if(gondolaSeq[i] <= n) offs = (n+i-gondolaSeq[i]+1) % n;
else expect[gondolaSeq[i]] = i;
if(gondolaSeq[i] > mx){
mx = gondolaSeq[i];
dummy = i;
}
}
for(int i = 0; i < n; i++){
initSeq[(i+offs) % n] = i+1;
}
int rpidx = 0;
for(int i = n+1; i <= mx; i++){
if(expect[i] == -1){
replacementSeq[rpidx++] = initSeq[dummy];
initSeq[dummy] = i;
}else{
replacementSeq[rpidx++] = initSeq[expect[i]];
initSeq[expect[i]] = i;
}
}
return rpidx;
}
int countReplacement(int n,int inputSeq[])
{
memset(ST,0,sizeof ST);
vector<int>b(n),cur;
for(int i=0;i<n;i++) inputSeq[i]--;
int res=0;
int val=0;
sort(inputSeq,inputSeq+n);
//for(int j=1;j<n;j++) if(inputSeq[j]==inputSeq[j-1]) return 0;
for(int j=0;j<n;j++) if(inputSeq[j]>(n-1)) cur.push_back(inputSeq[j]-n+1);
if(cur.empty()) val=1;
else
{
sort(cur.begin(),cur.end());
int sz=cur.size();
val=Power(sz,cur[0]-1);
for(int j=1;j<sz;j++)
{
if(cur[j]==cur[j-1])
{
val=0;
break;
}
val=1ll*val*Power(sz-j,cur[j]-cur[j-1]-1)%mod;
}
}
for(int i=0;i<n;i++) update(1,0,n-1,i,i,inputSeq[i]-i);
for(int i=0;i<n;i++)
{
dolazy(1,0,n-1);
if(ST[1]>=0) res=(res+val)%mod;
update(1,0,n-1,0,n-1,-1);
update(1,0,n-1,n-1-i,n-1-i,n);
}
return res;
}
int valid(int n,int inputSeq[])
{
return countReplacement(n,inputSeq)!=0;
}
/*
int main()
{
ios_base::sync_with_stdio(false);
cin.tie(nullptr);
int n;
cin>>n;
int a[n];
for(int i=0;i<n;i++) cin>>a[i];
cout<<countReplacement(n,a);
}
*/
