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*/
#include<bits/stdc++.h>
#include "gondola.h"
using namespace std;
typedef long long ll ;
const ll oo = 4294967296 ;
const double PI = acos(-1) ;
const ll M = 1e9 + 9 ;
map<int,int> mp;
vector<pair<int,int>> v;
pair<int, int> p[1000010] , rp[1000010] ;
int valid(int n, int inputSeq[]){
return -1 ;
}
// ----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[]){
return -2;
}
//----------------------
ll fastpower( ll x , ll n ){
ll res = 1 ;
while(n > 0){
if(n % 2 == 1)
res = (res * x) % M;
x = ( x * x ) % M;
n = n / 2 ;
}
return res;
}
int countReplacement(int n, int inputSeq[]){
bool b = false ;
for(int i = 0 ; i < n ; ++i){
p[i] = {inputSeq[i] , i + 1};
rp[i] = {inputSeq[i] , n - i};
mp[inputSeq[i]]++;
if(mp[inputSeq[i]] > 1)return 0;
if(inputSeq[i] <= n){
b = 1;
int x = inputSeq[i];
int f = i - 1;
while(f > -1 && inputSeq[f] > n){
x--;
if(x == 0) x = n;
v.push_back({inputSeq[f] , x});
inputSeq[f] = x;
mp[x]++;
if(mp[x] > 1) return 0 ;
f--;
}
f = i + 1 ;
x = inputSeq[i];
while(f < n && inputSeq[f] > n){
x++;
if(x == n + 1) x = 1;
v.push_back({inputSeq[f] , x});
inputSeq[f] = x;
mp[x]++;
if(mp[x] > 1)return 0;
f++;
}
i = f - 1;
}
}
ll ans = 1 , ls = n + 1 , ans1 = 1;
if(b){
for(int i = 1 ; i < n ; ++i)
if((inputSeq[i] == 1 && inputSeq[i - 1] != n) || (inputSeq[i] != 1 && inputSeq[i - 1] + 1 != inputSeq[i])) return 0;
sort(v.begin(), v.end());
int idx = 0 ;
for(auto x : v){
if(x.first == v.back().first) continue ;
ans = (ans * fastpower(v.size() - idx , x.first - ls)) % M;
ls = x.first + 1 ;
idx++;
}
}else{
int idx = 0 ;
sort(p , p + n);
sort(rp , rp + n);
for(int i = 0 ; i < n - 1 ; ++i){
ans = (ans * fastpower(v.size() - idx , p[i].first - ls)) % M;
ls = p[i].first + 1;
idx++;
}
idx = 0;
ls = n + 1;
for(int i = 0 ; i < n - 1 ; ++i){
ans1 = (ans1 * fastpower(v.size() - idx , p[i].first - ls)) % M;
idx++;
ls = p[i].first + 1;
}
ans = (ans + ans1) % M;
}
return ans ;
}
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