#include "gondola.h"
#include <map>
#include <set>
#define N 100000
#define MOD 1000000009
using namespace std;
int n, g_num, replace_num[N], out_temp[N];
long long count_tot = 1;
map<int, int> valid_w;
set<int> check;
bool valid_check(int x) {
set<int>::iterator it = check.lower_bound(x);
if (it == check.end() || *it != x) return false;
return true;
}
int valid(int _n, int in[]) {
bool g_check = false;
n = _n;
for (int i = 0; i < n; i++) {
if (g_check) {
g_num = g_num == n ? 1 : g_num + 1;
}
if (valid_check(in[i])) return 0;
valid_w[in[i]] = i, check.insert(in[i]);
if (in[i] <= n) {
if (g_check && g_num != in[i]) return 0;
else if (!g_check) {
g_check = true, g_num = in[i];
}
}
}
return 1;
}
int replacement(int _n, int in[], int out[]) {
int out_len = 0, w, k = _n + 1;
long long cnt = 0;
if (!valid(_n, in)) return -1;
for (int i = 0; i < n; i++) {
g_num = g_num == n ? 1 : g_num + 1;
replace_num[i] = g_num;
if (in[i] > n) cnt++;
}
if (cnt == n) count_tot *= (long long)n;
for (int i = 0; i < n; i++) {
w = replace_num[i];
while (k <= in[i]) {
if (!valid_check(k)) {
out[out_len++] = w;
w = k++;
count_tot *= cnt, count_tot %= MOD;
}
else if (valid_w[k] == i) {
out[out_len++] = w;
w = k++, cnt--;
}
else {
out[out_len++] = replace_num[valid_w[k]];
k++, cnt--;
}
}
} return out_len;
}
int countReplacement(int _n, int in[]) {
if (replacement(_n, in, out_temp) < 0) return 0;
return (int)count_tot;
}
