#include "gondola.h"
#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
#define ll long long
#define ld long double
#define ull unsigned long long
#define ff first
#define ss second
#define pii pair<int,int>
#define pll pair<long long, long long>
#define vi vector<int>
#define vl vector<long long>
#define pb push_back
#define rep(i, b) for(int i = 0; i < (b); ++i)
#define rep2(i,a,b) for(int i = a; i <= (b); ++i)
#define rep3(i,a,b,c) for(int i = a; i <= (b); i+=c)
#define count_bits(x) __builtin_popcountll((x))
#define all(x) (x).begin(),(x).end()
#define siz(x) (int)(x).size()
#define forall(it,x) for(auto& it:(x))
using namespace __gnu_pbds;
using namespace std;
typedef tree<int, null_type, less<int>, rb_tree_tag,tree_order_statistics_node_update> ordered_set;
mt19937 mt;void random_start(){mt.seed(chrono::time_point_cast<chrono::milliseconds>(chrono::high_resolution_clock::now()).time_since_epoch().count());}
ll los(ll a, ll b) {return a + (mt() % (b-a+1));}
const int INF = 1e9+50;
const ll INF_L = 1e18+40;
const ll MOD = 1e9+9;
bool was = 0;
ll fast_power(ll x, ll p)
{
ll ans = 1;
rep2(bit,0,30)
{
if(p & (1 << bit))
{
ans *= x;
ans %= MOD;
}
x *= x;
x %= MOD;
}
return ans;
}
int countReplacement(int n, int inputSeq[])
{
int step = 0;
vi arr(n);
rep(i,n)
{
if(inputSeq[i] <= n)
{
step = (inputSeq[i]-(i+1) + n) % n;
}
}
rep(i,n)
{
arr[(i+step)%n] = inputSeq[i];
}
rep(i,n)
{
if(arr[i] <= n && i+1 != arr[i])
{
was = 0;
return 0;
}
}
ll ways = 1;
vi vals;
rep(i,n)
{
if(arr[i] > n) vals.pb(arr[i]);
}
sort(all(vals));
ll prev = n;
rep(i,siz(vals))
{
ways *= fast_power(siz(vals)-i,vals[i]-prev-1);
ways %= MOD;
prev = vals[i];
}
return ways;
}
int valid(int n, int inputSeq[])
{
was = 1;
countReplacement(n,inputSeq);
if(was)
{
return 1;
}
return 0;
}
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
vector<pii> vals;
int step = 0;
rep(i,n)
{
if(gondolaSeq[i] <= n)
{
step = (gondolaSeq[i]-(i+1) + n) % n;
}
}
rep(i,n)
{
if(gondolaSeq[i] > n)
{
vals.pb({gondolaSeq[i],(i+step)%n+1});
}
}
int cur = n+1;
sort(all(vals));
int cur_val = 0;
int cur_ind = 0;
while(cur_val < siz(vals))
{
if(cur <= vals[cur_val].ff)
{
replacementSeq[cur_ind++] = vals[cur_val].ss;
cur++;
}
else cur_val++;
}
return cur_ind;
}
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