#include "gondola.h"
#include <algorithm>
#include <map>
using namespace std;
map<int,bool> Map;
int valid(int n, int inputSeq[])
{
int i;
int s,t;
s = -1;
for(i=0; i<n; i++){
if(Map.find(inputSeq[i]) != Map.end()) return 0;
Map[inputSeq[i]] = true;
if(inputSeq[i] <= n){
t = i+2-inputSeq[i];
if(t <= 0) t += n;
if(s == -1){
s = t;
}else if(s != t){
return 0;
}
}
}
return 1;
}
//----------------------
struct datar{
int num,value;
}a[100002];
bool cmp(datar x,datar y){
return x.value < y.value;
}
int first[100002];
int replacement(int n, int gondolaSeq[], int replacementSeq[])
{
int i,j,cnt;
int s,t,big,nnum;
s = -1;
for(i=0; i<n; i++){
if(gondolaSeq[i] <= n){
t = i+2-gondolaSeq[i];
if(t <= 0) t += n;
s = t;
break;
}
}
big = 0;
for(i=0; i<n; i++) big = max(big,gondolaSeq[i]);
if(big == n){
return 0;
}
for(i=n; i>=1; i--) gondolaSeq[i] = gondolaSeq[i-1];
cnt = 0;
if(s == -1) s = 1;
first[s] = 1;
for(i=1; i<n; i++){
t = s+i;
if(t > n) t -= n;
first[t] = i+1;
}
for(i=1; i<=n; i++){
a[i].num = i;
a[i].value = gondolaSeq[i];
}
sort(a+1,a+n+1,cmp);
nnum = n+1;
if(a[1].value > n){
replacementSeq[cnt] = first[a[1].num];
cnt++; nnum++;
for(i=nnum; i<=a[1].value; i++){
replacementSeq[cnt] = nnum-1;
cnt++; nnum++;
}
}
for(i=2; i<=n; i++){
if(a[i].value <= n) continue;
replacementSeq[cnt] = first[a[i].num]; cnt++; nnum++;
for(j=nnum; j<=a[i].value; j++){
replacementSeq[cnt] = nnum-1;
cnt++; nnum++;
}
}
return cnt;
}
//----------------------
#define MOD 1000000009;
long long mul(long long x,long long y){ // return x^y;
if(y == 0) return 1;
if(y == 1) return x;
long long tmp = mul(x,y/2);
tmp *= tmp; tmp %= MOD;
if(y%2 == 1){
tmp *= x;
tmp %= MOD;
}
return tmp;
}
long long ans;
int countReplacement(int n, int inputSeq[])
{
if(valid(n,inputSeq) == 0) return 0;
int i,j,t;
int s,big;
long long x,nnum;
s = -1;
for(i=0; i<n; i++){
if(inputSeq[i] <= n){
s = i+2-inputSeq[i];
if(s <= 0) s += n;
break;
}
}
big = 0;
for(i=0; i<n; i++) big = max(big,inputSeq[i]);
if(big == n){
return 1;
}
if(s == -1){
s = 1;
ans = (long long)n;
}else ans = 1;
for(i=n; i>=1; i--) inputSeq[i] = inputSeq[i-1];
first[s] = 1;
for(i=1; i<n; i++){
t = s+i;
if(t > n) t -= n;
first[t] = i+1;
}
for(i=1; i<=n; i++){
a[i].num = i;
a[i].value = inputSeq[i];
}
sort(a+1,a+n+1,cmp);
nnum = n+1;
x = (long long)n;
if(a[1].value > n){
nnum++;
ans *= mul(x,(long long)(a[1].value-nnum+1));
ans %= MOD;
nnum = a[1].value+1;
}
x--;
for(i=2; i<=n; i++){
if(a[i].value <= n){
x--;
continue;
}
nnum++;
ans *= mul(x,(long long)(a[i].value-nnum+1));
ans %= MOD;
nnum = a[i].value+1;
x--;
}
return (int)ans;
}
