#include <bits/stdc++.h>
using namespace std;
#ifdef tabr
#include "library/debug.cpp"
#else
#define debug(...)
#endif
#include "gondola.h"
template <long long mod>
struct modular {
long long value;
modular(long long x = 0) {
value = x % mod;
if (value < 0) value += mod;
}
modular& operator+=(const modular& other) {
if ((value += other.value) >= mod) value -= mod;
return *this;
}
modular& operator-=(const modular& other) {
if ((value -= other.value) < 0) value += mod;
return *this;
}
modular& operator*=(const modular& other) {
value = value * other.value % mod;
return *this;
}
modular& operator/=(const modular& other) {
long long a = 0, b = 1, c = other.value, m = mod;
while (c != 0) {
long long t = m / c;
m -= t * c;
swap(c, m);
a -= t * b;
swap(a, b);
}
a %= mod;
if (a < 0) a += mod;
value = value * a % mod;
return *this;
}
friend modular operator+(const modular& lhs, const modular& rhs) { return modular(lhs) += rhs; }
friend modular operator-(const modular& lhs, const modular& rhs) { return modular(lhs) -= rhs; }
friend modular operator*(const modular& lhs, const modular& rhs) { return modular(lhs) *= rhs; }
friend modular operator/(const modular& lhs, const modular& rhs) { return modular(lhs) /= rhs; }
modular& operator++() { return *this += 1; }
modular& operator--() { return *this -= 1; }
modular operator++(int) {
modular res(*this);
*this += 1;
return res;
}
modular operator--(int) {
modular res(*this);
*this -= 1;
return res;
}
modular operator-() const { return modular(-value); }
bool operator==(const modular& rhs) const { return value == rhs.value; }
bool operator!=(const modular& rhs) const { return value != rhs.value; }
bool operator<(const modular& rhs) const { return value < rhs.value; }
};
template <long long mod>
string to_string(const modular<mod>& x) {
return to_string(x.value);
}
template <long long mod>
ostream& operator<<(ostream& stream, const modular<mod>& x) {
return stream << x.value;
}
template <long long mod>
istream& operator>>(istream& stream, modular<mod>& x) {
stream >> x.value;
x.value %= mod;
if (x.value < 0) x.value += mod;
return stream;
}
constexpr long long mod = (long long) 1e9 + 9;
using mint = modular<mod>;
mint power(mint a, long long n) {
mint res = 1;
while (n > 0) {
if (n & 1) {
res *= a;
}
a *= a;
n >>= 1;
}
return res;
}
vector<mint> fact(1, 1);
vector<mint> finv(1, 1);
mint C(int n, int k) {
if (n < k || k < 0) {
return mint(0);
}
while ((int) fact.size() < n + 1) {
fact.emplace_back(fact.back() * (int) fact.size());
finv.emplace_back(mint(1) / fact.back());
}
return fact[n] * finv[k] * finv[n - k];
}
int valid(int n, int s[]) {
set<int> st;
for (int i = 0; i < n; i++) {
if (st.count(s[i])) {
return 0;
}
st.emplace(s[i]);
}
int pos = -1;
for (int i = 0; i < n; i++) {
if (s[i] <= n) {
pos = (i - s[i] + 1 + n) % n;
break;
}
}
for (int i = 0; i < n; i++) {
if (s[i] <= n) {
if (pos != (i - s[i] + 1 + n) % n) {
return 0;
}
}
}
return 1;
}
int replacement(int n, int s[], int res[]) {
int pos = -1;
for (int i = 0; i < n; i++) {
if (s[i] <= n) {
pos = (i - s[i] + 1 + n) % n;
}
}
vector<int> order(n);
iota(order.begin(), order.end(), 0);
sort(order.begin(), order.end(), [&](int i, int j) { return s[i] < s[j]; });
int id = 0;
int lst = n;
for (int i : order) {
if (s[i] <= n) {
continue;
}
int j = (i - pos + n) % n + 1;
res[id++] = j;
for (int x = lst + 2; x <= s[i]; x++) {
res[id++] = x - 1;
}
lst = s[i];
}
return id;
}
int countReplacement(int n, int s[]) {
if (!valid(n, s)) {
return 0;
}
sort(s, s + n);
mint ans = 1;
int lst = n;
for (int i = 0; i < n; i++) {
if (s[i] <= n) {
continue;
}
ans *= power(n - i, s[i] - lst - 1);
lst = s[i];
}
return (int) ans.value;
}
