#include "gondola.h"
#include <bits/stdc++.h>
#define fr first
#define sc second
#define pb push_back
#define mk make_pair
#define all(s) s.begin(), s.end()
using namespace std;
const int N = 3e5 + 5, mod = 1e9 + 9;
int sz, mx, pos, ind[N], ar[N], n, fl;
deque <pair <int, int> > vec;
map <int, int> u;
int valid(int N, int x[])
{
n = N;
for (int i = 0; i < n; i++)
{
if (u.count(x[i]))
return 0;
u[x[i]] = i + 1;
}
for (int i = 1; i < n; i++)
{
if ( u[i] != 0 && u[i + 1] != 0 && ((u[i] - 1) + 1) % n != u[i + 1] - 1)
return 0;
}
if ( u[n] != 0 && u[1] != 0 && ((u[n] - 1) + 1) % n != u[1] - 1)
return 0;
return 1;
}
int replacement(int n, int a[], int ans[])
{
for (int i = 0; i < n; i++)
mx = max(a[i], mx);
for (int i = 0; i < n; i++)
{
if(a[i] > n)
vec.pb( mk(a[i], i) );
else
pos = (i - (a[i] - 1) + n) % n;
}
sort( all(vec) );
ind[pos] = ++sz;
for (int i = (pos + 1) % n; i != pos; i = (i + 1) % n)
ind[i] = ++sz;
sz = 0;
for (int i = n + 1; i <= mx; i++)
{
ans[sz++] = ind[ vec[0].second ];
ind[ vec[0].second ] = i;
if ( vec[0].first == i )
vec.pop_front();
}
return sz;
}
int countReplacement(int n, int a[])
{
long long ans = 1;
if (valid(n, a) == 0)
return 0;
for (int i = 0; i < n; i++)
mx = max(a[i], mx);
for (int i = 0; i < n; i++)
{
if(a[i] > n)
vec.pb( mk(a[i], i) );
else
pos = (i - (a[i] - 1) + n) % n, fl = 1;
}
sort( all(vec) );
int L = n + 1;
sz = vec.size();
for (auto to : vec)
{
if (to.first != L)
ans *= (to.first - L) * 1ll * sz % mod,
ans %= mod;
L = to.first + 1;
sz--;
}
if (!fl)
ans *= n, ans %= mod;
return ans;
}
/**
9
4
1 2 7 6
**/
