#include <bits/stdc++.h>
#include "gondola.h"
#define maxn 100003
#define maxv 250001
#define mod 1000000009
using namespace std;
typedef long long LL;
int idx[maxv];
int init[maxn];
void calcInit(int n, int inputSeq[], int minIdx) {
if(minIdx == -1)
for( int i = 0 ; i < n ; i++ )
init[i] = i+1;
else
for( int i = 0 ; i < n ; i++ ) {
int d = (i-minIdx+n) % n;
init[i] = inputSeq[minIdx]+d;
if(init[i] > n)
init[i] -= n;
}
}
int valid(int n, int inputSeq[]) {
int minIdx = -1;
set<int> s;
for( int i = 0 ; i < n ; i++ ) {
if(s.find(inputSeq[i]) != s.end())
return 0;
s.insert(inputSeq[i]);
if(inputSeq[i] <= n) {
if(minIdx == -1 || inputSeq[i] < inputSeq[minIdx])
minIdx = i;
}
}
calcInit(n,inputSeq,minIdx);
if(minIdx == -1)
return 1;
for( int i = 0 ; i < n ; i++ )
if(inputSeq[i] <= n)
if(init[i] != inputSeq[i])
return 0;
return 1;
}
int replacement(int n, int inputSeq[], int replacementSeq[]) {
if(!valid(n,inputSeq))
return 0;
int maxIdx = -1;
memset(idx,-1,sizeof(idx));
for( int i = 0 ; i < n ; i++ ) {
idx[inputSeq[i]] = i;
if(maxIdx == -1 || inputSeq[i] > inputSeq[maxIdx])
maxIdx = i;
}
int cnt = 0;
int curr = init[maxIdx];
int maxVal = inputSeq[maxIdx];
for( int i = n+1 ; i <= maxVal ; i++ ) {
if(idx[i] == -1 || i == maxVal) {
replacementSeq[cnt++] = curr;
curr = i;
}
else
replacementSeq[cnt++] = init[idx[i]];
}
return cnt;
}
LL calcPow(LL x , int y) {
if(y == 0)
return 1;
LL val = calcPow(x,y/2);
val = (val*val) % mod;
if(y & 1)
val = (val*x) % mod;
return val;
}
int countReplacement(int n, int inputSeq[]) {
if(!valid(n,inputSeq))
return 0;
sort(inputSeq,inputSeq+n);
int last = n;
LL ans = 1;
for( int i = 0 ; i < n ; i++ )
if(inputSeq[i] > last) {
int diff = inputSeq[i]-last-1;
int base = n-i;
last = inputSeq[i];
LL mult = calcPow(base,diff);
ans = (ans*mult) % mod;
}
if(inputSeq[0] > n)
ans = (ans*n) % mod;
return (int) ans;
}
/*
int main() {
int n = 2;
int inputSeq[n] = {3,4};
int res = countReplacement(n,inputSeq);
printf("res = %d\n",res);
return 0;
}
*/
