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#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
const int Nmax = 250005, Mod = 1e9 + 9;
typedef long long ll;
int a[Nmax];
int valid(int n, int A[])
{
map<int,int> ap;
int i, rot = Mod;
for(i=0; i<n; ++i)
if(A[i] <= n)
{
if(rot == Mod) rot = (n + i - A[i]) % n;
else if(rot != (n + i - A[i]) % n) return 0;
}
else ++ap[i];
for(auto it : ap)
if(it.second > 1) return 0;
return 1;
}
bool cmp(int x, int y)
{
return a[x] < a[y];
}
int replacement(int n, int A[], int ans[])
{
int i, last = n+1, rot = 0;
vector<int> v;
for(i=0; i<n; ++i)
if(A[i] <= n) rot = (A[i] - 1) - i;
if(rot < 0) rot += n;
for(i=0; i<n; ++i) a[(i + rot) % n] = A[i];
for(i=0; i<n; ++i)
if(a[i] > n) v.push_back(i);
sort(v.begin(), v.end(), cmp);
int nr = 0;
for(auto it : v)
{
ans[nr++] = it+1;
for(i=last; i<a[it]; ++i) ans[nr++] = i;
last = a[it];
}
return nr;
}
ll power(ll a, int b)
{
ll ans = 1;
while(b)
{
if(b&1) ans = ans * a % Mod;
a = a * a % Mod; b >>= 1;
}
return ans;
}
int countReplacement(int n, int A[])
{
if(!valid(n, A)) return 0;
int i;
vector<int> v;
for(i=0; i<n; ++i)
if(A[i] > n) v.push_back(A[i] - n);
sort(v.begin(), v.end());
int m = v.size();
ll ans = 1;
int last = 0;
for(auto it : v)
{
ans *= power(m, it - last - 1);
ans %= Mod;
--m;
last = it;
}
return (int) ans;
}
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