#include "gondola.h"
#include <bits/stdc++.h>
using namespace std;
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<typename T> using ordered_set = tree<T, null_type, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
template<typename T, typename U> using ordered_map = tree<T, U, less<T>, rb_tree_tag, tree_order_statistics_node_update>;
typedef long long ll;
typedef long double ld;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef vector<int> vi;
typedef vector<ll> vll;
#define FOR(i,j,k,in) for(int i=(j); i < (k);i+=in)
#define FORD(i,j,k,in) for(int i=(j); i >=(k);i-=in)
#define REP(i,b) FOR(i,0,b,1)
#define REPD(i,b) FORD(i,b,0,1)
#define pb push_back
#define mp make_pair
#define ff first
#define ss second
#define all(x) begin(x), end(x)
#define MANY_TESTS int tcase; cin >> tcase; while(tcase--)
const double EPS = 1e-9;
const int MOD = 1e9+7;
const ll INFF = 1e18;
const int INF = 1e9;
const ld PI = acos((ld)-1);
const vi dy = {1, 0, -1, 0, -1, 1, 1, -1};
const vi dx = {0, 1, 0, -1, -1, 1, -1, 1};
void DBG(){cout << "]" << endl;}
template<typename T, typename ...U> void DBG(const T& head, const U... args){ cout << head << "; "; DBG(args...); }
#define dbg(...) cout << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__);
#define chk() cout << "Check at line(" << __LINE__ << ") hit." << endl;
template<class T, unsigned int U>
ostream& operator<<(ostream& out, const array<T, U> &v){out << "["; REP(i, U) out << v[i] << ", "; out << "]"; return out;}
template <class T, class U>
ostream& operator<<(ostream& out, const pair<T, U> &par) {out << "[" << par.first << ";" << par.second << "]"; return out;}
template <class T>
ostream& operator<<(ostream& out, const set<T> &cont) { out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template <class T, class U>
ostream& operator<<(ostream& out, const map<T, U> &cont) {out << "{"; for( const auto &x:cont) out << x << ", "; out << "}"; return out; }
template<class T>
ostream& operator<<(ostream& out, const vector<T> &v){ out << "["; REP(i, v.size()) out << v[i] << ", "; out << "]"; return out;}
template<class T>
istream& operator>>(istream& in, vector<T> &v){ for(auto &x : v) in >> x; return in; }
const int mx = (int)1e6 + 5;
int valid(int n, int inputSeq[])
{
vector<int> inp(n);
REP(i, n)
inp[i] = inputSeq[i];
auto rotate_seq = [&](){
int mini = min_element(all(inp)) - inp.begin();
rotate(inp.begin(), inp.begin() + mini, inp.end());
};
rotate_seq();
bool can = true;
int last = -1;
vector<int> cnt(mx, 0);
REP(i, inp.size()) cnt[inp[i]]++;
REP(i, mx){
if(cnt[i] > 1) can = false;
}
REP(i, inp.size()){
if(inp[i] <= n){
if(last != -1 && inp[i] != inp[last] + (i - last))
can = false;
last = i;
}
}
return (can ? 1 : 0);
}
//----------------------
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
vector<int> inp(n);
REP(i, n)
inp[i] = gondolaSeq[i];
auto rotate_seq = [&](){
int mini = min_element(all(inp)) - inp.begin();
if(inp[mini] > n) return;
int rot = mini - inp[mini] + 1;
if(rot < 0) rot += n;
rotate(inp.begin(), inp.begin() + rot, inp.end());
//rotate(inp.begin(), inp.begin() + mini, inp.end());
};
rotate_seq();
vector<int> pos(mx, -1);
REP(i, n){
pos[inp[i]] = i;
}
set<int> incorrect;
REP(i, n){
if(inp[i] != i + 1)
incorrect.insert(i);
}
int l = 0;
vector<int> narr(n);
iota(all(narr), 1);
FOR(i, n + 1, mx, 1){
if(incorrect.empty()) break;
if(pos[i] == -1){
replacementSeq[l] = narr[*incorrect.begin()];
narr[*incorrect.begin()] = i;
l++;
}
else{
replacementSeq[l] = narr[pos[i]];
incorrect.erase(pos[i]);
narr[pos[i]] = i;
l++;
}
}
return l;
}
//----------------------
const int mod = (int)1e9 + 9;
struct Mint{
ll v;
Mint(){v = 0;}
Mint(ll _v){
v = _v;
v%= mod;
if(v < 0) v += mod;
}
friend Mint operator*(Mint a, Mint b){
return Mint(a.v * b.v);
}
};
int countReplacement(int n, int inputSeq[])
{
vector<int> inp(n);
REP(i, n)
inp[i] = inputSeq[i];
auto check_validity = [](vector<int> inp, int n){
const int mx = (int)1e6 + 6;
auto rotate_seq = [&](){
int mini = min_element(all(inp)) - inp.begin();
rotate(inp.begin(), inp.begin() + mini, inp.end());
};
rotate_seq();
bool can = true;
int last = -1;
vector<int> cnt(mx, 0);
REP(i, inp.size()) cnt[inp[i]]++;
REP(i, mx){
if(cnt[i] > 1) can = false;
}
REP(i, inp.size()){
if(inp[i] <= n){
if(last != -1 && inp[i] != inp[last] + (i - last))
can = false;
last = i;
}
}
return (can ? 1 : 0);
};
if(!check_validity(inp, n)){
return 0;
}
auto rotate_seq = [&](){
int mini = min_element(all(inp)) - inp.begin();
if(inp[mini] > n) return;
int rot = mini - inp[mini] + 1;
if(rot < 0) rot += n;
rotate(inp.begin(), inp.begin() + rot, inp.end());
};
rotate_seq();
vector<int> pos(mx, -1);
REP(i, n){
pos[inp[i]] = i;
}
set<int> incorrect;
REP(i, n){
if(inp[i] != i + 1)
incorrect.insert(i);
}
Mint ans(1);
FOR(i, n + 1, mx, 1){
if(incorrect.empty()) break;
if(pos[i] == -1){
ans = ans * Mint(incorrect.size());
}
else{
incorrect.erase(pos[i]);
}
}
int diff = *min_element(all(inp)) - n;
Mint temp(1);
if(diff - 1 > 0){
REP(i, diff - 1){
temp = temp * Mint(n);
}
}
ans = ans * temp;
return (int)ans.v;
}
