#include <bits/stdc++.h>
#include "gondola.h"
using namespace std;
#ifdef ngu
#include "debug.h"
#else
#define debug(...) 42
#endif
const int N = 250005;
int cnt[N];
int shift(int i, int j, int n) {
i += j;
if (i < 1) {
i += n;
}
if (i > n) {
i -= n;
}
return i;
}
int valid(int n, int inputSeq[]) {
memset(cnt, 0, sizeof(cnt));
for (int i = 0; i < n; ++i) {
assert(inputSeq[i] < N);
if (cnt[inputSeq[i]]) {
return 0;
}
cnt[inputSeq[i]]++;
}
int delta = 0;
for (int i = 0; i < n; ++i) {
if (inputSeq[i] <= n) {
int j = inputSeq[i];
delta = j - i - 1;
break;
}
}
for (int i = 0; i < n; ++i) {
if (inputSeq[i] <= n) {
int j = shift(i + 1, delta, n);
if (j != inputSeq[i]) {
return 0;
}
}
}
return 1;
}
int pos[N];
int replacement(int n, int gondolaSeq[], int replacementSeq[]) {
memset(pos, -1, sizeof(pos));
for (int i = 0; i < n; ++i) {
pos[gondolaSeq[i]] = i;
}
set<int> cur;
for (int i = 0; i < n; ++i) {
cur.insert(i);
}
for (int i = 0; i < n; ++i) {
if (gondolaSeq[i] <= n) {
cur.erase(i);
}
}
int delta = 0;
for (int i = 0; i < n; ++i) {
if (gondolaSeq[i] <= n) {
int j = gondolaSeq[i];
delta = j - i - 1;
break;
}
}
for (int i = 0; i < n; ++i) {
gondolaSeq[i] = shift(i + 1, delta, n);
}
int m = -1;
for (int i = n + 1; i < N; ++i) {
if (!cur.size()) {
break;
}
int j = *cur.begin();
if (pos[i] != -1) {
j = pos[i];
cur.erase(j);
}
replacementSeq[++m] = gondolaSeq[j];
gondolaSeq[j] = i;
}
return m + 1;
}
const int MOD = (int) 1e9 + 9;
int bin_pow(int a, int b) {
int res = 1;
for (; b; b >>= 1, a = 1LL * a * a % MOD) {
if (b & 1) {
res = 1LL * res * a % MOD;
}
}
return res;
}
int countReplacement(int n, int inputSeq[]) {
set<int> pos;
for (int i = 0; i < n; ++i) {
if (pos.find(inputSeq[i]) != pos.end()) {
return 0;
}
pos.insert(inputSeq[i]);
}
int cnt = n;
for (int i = 0; i < n; ++i) {
if (inputSeq[i] <= n) {
cnt--;
pos.erase(inputSeq[i]);
}
}
int res = 1;
int delta = 0;
for (int i = 0; i < n; ++i) {
if (inputSeq[i] <= n) {
int j = inputSeq[i];
delta = j - i - 1;
break;
}
}
for (int i = 0; i < n; ++i) {
if (inputSeq[i] <= n && inputSeq[i] != shift(i + 1, delta, n)) {
return 0;
}
inputSeq[i] = shift(i + 1, delta, n);
}
if (cnt == n) {
res = 1LL * res * n % MOD;
}
int p = n;
for (int j : pos) {
res = 1LL * res * bin_pow(cnt, j - 1 - p) % MOD;
p = j;
cnt--;
}
return res;
}
