#include <bits/stdc++.h>
#include "gondola.h"
using namespace std;
typedef pair<int,int> pii;
#define fi first
#define se second
#define mp make_pair
const int N = (int)25e4 + 1293;
int valid(int n, int inputSeq[])
{
int cnt[N];
for(int j = 0;j < N;j ++ )
cnt[j] = 0;
int rest[n];
int maz = (int)4e5 + 12345;
for(int i = 0; i < n;i ++){
cnt[inputSeq[i]]++;
if(cnt[inputSeq[i]] >= 2)
return 0;
maz = min(maz, inputSeq[i]);
rest[i] = inputSeq[i];
}
if(maz > n)
return 1;
int p,j;
for(int i = 0;i < n;i ++ ){
if(rest[i] <= n){
p = rest[i]+1;
j = i+1;
j %= N;
while(p <= n){
rest[j] = p;
p++;
j++;
j%=n;
}
p = 1;
while(p < rest[i]){
rest[j] = p;
j++;
j %= n;
p++;
}
break;
}
}
for(int i = 0; i < n;i ++){
if(inputSeq[i] <= n){
if(rest[i] != inputSeq[i])
return 0;
}
}
return 1;
}
//----------------------
int replacement(int n, int gondolas[], int replacementSeq[])
{
int rx = 0;
int start[n];
bool is = false;
for(int i = 0;i < n;i ++){
if(gondolas[i] > n)
is = true;
if(gondolas[i] <= n)
rx = i;
}
if(is == false)
return 0;
int ini;
if(gondolas[rx] > n)
start[rx] = 1;
else
start[rx] = gondolas[rx];
int p = start[rx] + 1;
ini = start[rx];
rx ++ ;
while(p <= n){
rx %= n;
start[rx] = p;
rx++;
p++;
}
p = 1;
rx %= n;
while(p < ini){
start[rx] = p;
p++;
rx++;
rx %= n;
}
vector<pii>qq;
for(int i = 0;i < n;i ++){
if(start[i] < gondolas[i]){
qq.push_back(mp(gondolas[i],i));
}
}
sort(qq.begin(),qq.end());
int mak;
int ii = n + 1;
int ix;
int sz = 0;
for(auto x : qq){
mak = x.fi;
ix = x.se;
replacementSeq[sz] = start[ix];
sz++;
start[ix] = ii;
ii++;
while(start[ix] < mak){
replacementSeq[sz] = start[ix];
start[ix] = ii;
sz++;
ii++;
}
ii = mak + 1;
}
return sz;
}
//----------------------
const int MOD = (int)1e9 + 9;
int powr(int n,int k){
if(k == 0)
return 1;
int hf = powr(n,k/2);
hf = (1LL * hf * hf) % MOD;
if(k&1)
hf = (1LL * hf * n) % MOD;
return hf;
}
int countReplacement(int n, int inputSeq[])
{
if(!valid(n,inputSeq)){
return 0;
}
int ans = 1;
int mn = (int)1e9 + 999;
for(int i = 0;i < n;i ++)
mn = min(mn,inputSeq[i]);
if(mn > n)
ans = n; // n cylcic rotations
vector<int>nex;
nex.push_back(n);
for(int i = 0;i < n;i ++)
if(inputSeq[i] > n)
nex.push_back(inputSeq[i]);
sort(nex.begin(),nex.end());
int tk = (int)nex.size() - 1;
for(int i = 1;i < (int)nex.size(); i ++){
ans = (1LL * ans * powr(tk,nex[i] - nex[i - 1] - 1)) % MOD;
--tk;
}
return ans;
}
