#include<bits/stdc++.h>
#include "gondola.h"
#define F first
#define S second
#define PB push_back
#define sz(s) (int(s.size()))
#define bit(n, k) (((n)>>(k))&1)
using namespace std;
typedef long long ll;
typedef pair<int, int> pii;
typedef long double ld;
const int maxn = 1e5 + 10, mod = 1e9 + 7;
int valid(int n, int inp[]){
int pos[n];
fill(pos, pos + n, -1);
set<int> st;
for(int i = 0; i < n; i++){
--inp[i];
if(inp[i] < 0)
return 0;
if(st.count(inp[i]))
return 0;
st.insert(inp[i]);
if(inp[i] < n)
pos[inp[i]] = i;
}
int lst = -1;
for(int i = 0; i < n; i++){
if(pos[i] != -1){
if(lst == -1)
lst = i;
if((lst - i + n) % n != (pos[lst] - pos[i] + n) % n)
return 0;
}
}
for(int i = 0; i < n; i++){
if(pos[i] != -1){
if(lst == -1)
lst = i;
if((lst - i + n) % n != (pos[lst] - pos[i] + n) % n)
return 0;
}
}
return 1;
}
int replacement(int n, int inp[], int outp[]){
const int maxl = 3e5 + 10;
int pos[maxl], arr[n];
memset(pos, -1, sizeof pos);
int start = 0;
for(int i = 0; i < n; i++){
pos[--inp[i]] = i;
if(inp[i] < n)
start = (i - inp[i] + n) % n;
}
for(int i = 0; i < n; i++){
arr[(i + start) % n] = i;
}
set<int> fre;
for(int i = 0; i < n; i++){
if(inp[i] >= n)
fre.insert(i);
}
int L = 0;
for(int i = n; i < maxl; i++){
if(pos[i] == -1){
if(fre.empty())
break;
int x = *fre.begin();
outp[L++] = arr[x] + 1;
arr[x] = i;
}
else{
fre.erase(pos[i]);
int x = pos[i];
outp[L++] = arr[x] + 1;
arr[x] = i;
}
}
return L;
}
int Pow(int a, int b, int mod){
int ans = 1;
for(; b; b>>=1, a = 1ll * a * a % mod)
if(b & 1)
ans = 1ll * ans * a % mod;
return ans;
}
int countReplacement(int n, int inp[]){
int chert[n + 10];
for(int i = 0; i < n; i++)
chert[i] = inp[i];
if(!valid(n, chert))
return 0;
const int mod = 1e9 + 9;
map<int, int> pos;
int ans = 1;
int start = -1;
for(int i = 0; i < n; i++){
pos[--inp[i]] = i;
if(inp[i] < n)
start = (i - inp[i] + n) % n;
}
if(start == -1)
ans = n;
int fre = 0;
for(int i = 0; i < n; i++){
if(inp[i] >= n)
fre++;
}
int lst = n-1;
for(pii p : pos){
if(p.F < n)
continue;
ans = 1ll * ans * Pow(fre, p.F - lst - 1, mod) % mod;
lst = p.F, fre--;
}
return ans;
}
