#include "gondola.h"
#include <bits/stdc++.h>
#define ll long long
#define endl "\n"
using namespace std;
const ll mod = 1e9 + 9;
ll binpow(ll n, ll p)
{
ll ans = 1;
n %= mod;
while (p)
{
ans = (p & 1 ? ans * n % mod : ans);
p >>= 1;
n = n * n % mod;
}
return ans;
}
int valid(int n, int a[])
{
set<ll> s;
for (ll i = 0; i < n; i++)
s.insert(a[i]);
if (s.size() != n)
return 0;
ll st = -1, b[n];
for (ll i = 0; i < n; i++)
if (a[i] <= n)
st = i;
if (st == -1)
return 1;
b[st] = a[st];
for (ll i = st + 1; i < st + n; i++)
b[i % n] = b[(i - 1 + n) % n] % n + 1;
// for (ll i = 0; i < n; i++)
// cout << b[i] << " ";
// cout << endl;
for (ll i = 0; i < n; i++)
if (a[i] <= n and a[i] != b[i])
return 0;
return 1;
}
//----------------------
int replacement(int n, int a[], int replacementSeq[])
{
ll st = -1, b[n];
for (ll i = 0; i < n; i++)
if (a[i] <= n)
st = i;
if (st == -1)
iota(b, b + n, 1);
else
{
b[st] = a[st];
for (ll i = st + 1; i < st + n; i++)
b[i % n] = b[(i - 1 + n) % n] % n + 1;
}
ll ptr = 0, mx = max_element(a, a + n) - a;
ll ind[a[mx] + 1];
for (ll i = 0; i <= a[mx]; i++)
ind[i] = -1;
for (ll i = 0; i < n; i++)
ind[a[i]] = i;
for (ll i = n + 1; i <= a[mx]; i++)
if (ind[i] != -1)
replacementSeq[ptr++] = b[ind[i]], b[ind[i]] = i;
else
replacementSeq[ptr++] = b[mx], b[mx] = i;
return ptr;
}
//----------------------
int countReplacement(int n, int a[])
{
if (!valid(n, a))
return 0;
ll ans = 1;
ll b[n];
for (ll i = 0; i < n; i++)
b[i] = a[i];
sort(b, b + n, greater());
for (ll i = 0; i < n and b[i] > n; i++)
ans = ans * binpow(i + 1, b[i] - max((ll)n, i + 1 < n ? b[i + 1] : 1) - 1) % mod;
if (b[n - 1] > n)
ans = ans * n % mod;
return ans;
}
