This submission is migrated from previous version of oj.uz, which used different machine for grading. This submission may have different result if resubmitted.
///~~~LOTA~~~///
#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#define nl '\n'
#define ff first
#define ss second
#define ll long long
#define append push_back
#define pii pair<int,int>
#define all(x) (x).begin(),(x).end()
#define MAXN 250001
ll mod=1e9+9;
int vis[MAXN];
int valid(int n, int a[]){
for(int i=0;i<n;i++){
if(a[i]>n) continue;
vis[a[i]]=1;
for(int j=i+1;j<i+n;j++){
if(vis[a[j%n]]) return 0;
vis[a[j%n]]=1;
if(a[j%n]>n) continue;
if(a[j%n]!=1+((a[i]+j-i-1)%n)) return 0;
}
return 1;
}
for(int i=0;i<n;i++){
if(vis[a[i]]) return 0;
vis[a[i]]=1;
}
return 1;
}
int replacement(int n,int a[],int v[]){
int m,o;
set<pii> s;
for(int i=m=o=0;i<n;i++){
m=max(m,a[i]);
if(a[i]>n) continue;
for(int j=i+1;j<i+n;j++){
m=max(m,a[j%n]);
if(a[j%n]>n)
s.insert({a[j%n],1+((a[i]+j-i-1)%n)});
}
o=1;
break;
}
pii pi;
if(!o)
for(int i=0;i<n;i++)
s.insert({a[i],i+1});
o=0;
for(int i=n+1;i<=m;i++){
pi=*s.begin();
s.erase(s.begin());
v[o]=pi.ss;
pi.ss=i;
o++;
if(pi.ss!=pi.ff)
s.insert(pi);
}
return o;
}
int countReplacement(int n,int a[]){
if(!valid(n,a)) return 0;
int m;
set<int> s;
for(int i=m=0;i<n;i++){
m=max(m,a[i]);
if(a[i]>n) s.insert(a[i]);
}
ll o=1;
for(int i=n+1;i<=m;i++){
if(*s.begin()==i)
s.erase(s.begin());
else o=(o*s.size())%mod;
}
return o;
}
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