#include "gondola.h"
#include <map>
#include <set>
#include <algorithm>
#define N 100001
#define MOD 1000000009
using namespace std;
int n, g_num, replace_num[N];
int d_len, d[N];
long long count_tot = 1, multi[100], multi_num[100];
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;
valid(_n, in);
for (int i = 0; i < n; i++) {
g_num = g_num == n ? 1 : g_num + 1;
replace_num[i] = g_num;
}
for (int i = 0; i < n; i++) {
w = replace_num[i];
while (k <= in[i]) {
if (valid_w[k] && valid_w[k] != i) {
out[out_len++] = replace_num[valid_w[k]];
k++;
}
else {
out[out_len++] = w;
w = k++;
}
}
} return out_len;
}
long long f(long long x, long long turn) {
int k = 1;
long long res = 1;
multi[0] = 1, multi_num[0] = 0;
multi[1] = x, multi_num[1] = 1;
while (multi_num[k] < turn) {
k++;
multi[k] = (multi[k - 1] * multi[k - 1]) % MOD;
multi_num[k] = multi_num[k - 1] * 2;
}
for(int i=k; i>=1; i--)
if (turn >= multi_num[i]) {
turn -= multi_num[i];
res = (res*multi[i]) % MOD;
}
return res;
}
int countReplacement(int _n, int in[]) {
if (!valid(_n, in)) return 0;
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) d[++d_len] = in[i];
}
if (d_len == n) count_tot = (long long)n;
sort(d + 1, d + d_len + 1);
int k = n + 1;
for (int i = 1; i <= d_len; i++) {
count_tot *= f(d_len - i + 1, d[i] - k);
count_tot %= MOD, k = d[i] + 1;
} return count_tot;
}
