#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
using ll = long long;
const int mod = 1e9 + 9;
int mul(int a, int b) {
return a * 1LL * b % mod;
}
int binpow(int a, int b) {
int res = 1;
while(b > 0) {
if(b & 1) res = mul(res, a);
a = mul(a, a);
b >>= 1;
}
return res;
}
int valid(int n, int s[]) {
set<int> st(s, s + n);
if( (int)st.size() != n ) return false;
st.clear();
for(int i = 0; i < n; i++) {
s[i]--;
if(s[i] < n) {
st.emplace((i - s[i] + n) % n);
}
}
return (int)st.size() <= 1;
}
//----------------------
int replacement(int n, int s[], int r[]) {
int add = 0;
vector<array<int, 2>> b;
for(int i = 0; i < n; i++) {
s[i]--;
if(s[i] < n) {
add = (s[i] - i + n) % n;
} else {
b.push_back({s[i], i});
}
}
sort(b.begin(), b.end());
int l = 0, cur = n - 1;
for(auto [x, i] : b) {
r[l++] = (i + add) % n;
cur++;
while(cur < x) {
r[l++] = cur++;
}
}
for(int i = 0; i < l; i++) r[i]++;
return l;
}
//----------------------
int countReplacement(int n, int s[]) {
if( !valid(n, s) ) return 0;
vector<int> b;
for(int i = 0; i < n; i++) {
if(s[i] >= n) {
b.push_back(s[i]);
}
}
b.push_back(n - 1);
sort(b.begin(), b.end());
// for(auto &x : b) cout << x + 1 << ' ';
// cout << '\n';
int ans = 1;
for(int i = 1; i < (int)b.size(); i++) {
int aval = b.size() - i;
int k = b[i] - b[i - 1] - 1;
// cout << aval << ' ' << k << '\n';
ans = mul( ans, binpow(aval, k) );
}
if( (int)b.size() == n + 1 ) {
ans = mul(ans, n);
}
return ans;
}
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