#include "gondola.h"
#define MOD 1000000009
int n;
int g_num, valid_w[250001], replace_num[100000];
int out_temp[100000];
long long count_tot = 1;
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_w[in[i]]) return 0;
valid_w[in[i]] = i + 1;
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_w[k] && valid_w[k] != i+1) {
out[out_len++] = replace_num[valid_w[k]-1];
k++, cnt--;
}
else if (valid_w[k]) {
out[out_len++] = w;
w = k++, cnt--;
}
else {
out[out_len++] = w;
w = k++;
count_tot *= cnt, count_tot %= MOD;
}
}
} return out_len;
}
int countReplacement(int _n, int in[]) {
if (replacement(_n, in, out_temp) < 0) return 0;
return (int)count_tot;
}
