#include "gondola.h"
#pragma GCC optimize("O3")
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
typedef long double ld;
typedef pair < int, int > pii;
typedef pair < ll, ll > pll;
#define F first
#define S second
#define all(x) x.begin(), x.end()
#define SZ(x) (int)x.size()
#define Mp make_pair
#define endl "\n"
#define fast_io ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
const int N = 1e6 + 10;
const int LOG = 20;
const ll mod = 1e9 + 9;
const ll inf = 8e18;
ll pw(ll a, ll b)
{
if(a == 0) return 0;
ll ret = 1;
while(b)
{
if(b & 1)
{
ret = ret * a % mod;
}
a = a * a % mod;
b >>= 1;
}
return ret;
}
map < int, int > mark;
int valid(int n, int inputSeq[])
{
int id = -1;
for(int i = 0; i < n; i ++)
{
if(++ mark[inputSeq[i]] > 1) return 0;
if(inputSeq[i] <= n)
{
id = i;
}
}
if(id == -1) return 1;
int start = (id - (inputSeq[id] - 1) + n + n) % n;
for(int i = 0; i < n; i ++)
{
int j = (i + start) % n;
if(inputSeq[j] > n) continue;
if(inputSeq[j] != i + 1)
{
return 0;
}
}
return 1;
}
//----------------------
int replacement(int n, int A[], int replacementSeq[])
{
int Mx = 0;
int id = -1;
for(int i = 0; i < n; i ++)
{
Mx = max(Mx, A[i]);
mark[A[i]] ++;
if(A[i] <= n)
{
id = i;
}
}
vector < int > vec;
vec.push_back(Mx);
for(int i = Mx - 1; i > n; i --)
{
if(mark[i] > 2) return -1;
if(mark[i] == 0) vec.push_back(i);
}
int start;
if(id == -1) { start = 0; }
else { start = (id - (A[id] - 1) + n + n) % n; }
for(int i = 0; i < n; i ++)
{
int j = (start + i) % n;
if(A[j] <= n) continue;
///printf("i = %d j = %d\n", i, j);
if(A[j] != Mx) replacementSeq[A[j] - n - 1] = i + 1;
else
{
///printf("here i = %d j = %d\n", i, j);
int last = i + 1;
while(SZ(vec))
{
int l = vec.back();
///printf("here l = %d last = %d\n", l, last);
vec.pop_back();
replacementSeq[l - n - 1] = last;
last = l;
}
}
}
return Mx - n;
}
//----------------------
int countReplacement(int n, int A[])
{
ll ret = 1;
int id = -1;
vector < int > vec;
for(int i = 0; i < n; i ++)
{
mark[A[i]] ++;
if(mark[A[i]] > 1) return 0;
if(A[i] <= n)
{
id = i;
}
else
{
vec.push_back(A[i]);
}
}
vec.push_back(n);
sort(all(vec), greater < int > ());
for(int i = 1; i < SZ(vec); i ++)
{
ret = ret * pw(i, vec[i - 1] - vec[i] - 1) % mod;
}
int start;
if(id == -1)
{
ret = ret * n % mod;
return ret;
}
else { start = (id - (A[id] - 1) + n + n) % n; }
for(int i = 0; i < n; i ++)
{
int j = (start + i) % n;
if(A[j] > n) continue;
if(A[j] != i + 1) return 0;
}
return ret;
}
