Problem:
Score: 500 points

Problem Statement

N people are standing in a queue, numbered 1, 2, 3, ..., N from front to back. Each person wears a hat, which is red, blue, or green.

The person numbered i says:

"In front of me, exactly A_i people are wearing hats with the same color as mine."

Assuming that all these statements are correct, find the number of possible combinations of colors of the N people's hats.

Since the count can be enormous, compute it modulo 1000000007.

Constraints

1 \leq N \leq 100000

0 \leq A_i \leq N-1

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1 A_2 A_3 ... A_N

Output

Print the number of possible combinations of colors of the N people's hats, modulo 1000000007.

Sample Input 1

6
0 1 2 3 4 5

Sample Output 1

3

We have three possible combinations, as follows:

Red, Red, Red, Red, Red, Red

Blue, Blue, Blue, Blue, Blue, Blue

Green, Green, Green, Green, Green, Green

Sample Input 2

3
0 0 0

Sample Output 2

6

Sample Input 3

54
0 0 1 0 1 2 1 2 3 2 3 3 4 4 5 4 6 5 7 8 5 6 6 7 7 8 8 9 9 10 10 11 9 12 10 13 14 11 11 12 12 13 13 14 14 15 15 15 16 16 16 17 17 17

Sample Output 3

115295190

Solution in C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
 
using namespace std;
 
#define FORE(i, a) for (auto i = a.begin(); i != a.end(); ++i)
#define REPU(i, a, b) for (int i = (a); i < (b); ++i)
#define REPD(i, a, b) for (int i = (a); i > (b); --i)
#define MEM(a, x) memset(a, x, sizeof(a))
#define ALL(a) a.begin(), a.end()
#define UNIQUE(a) a.erase(unique(ALL(a)), a.end())
 
vector<string> split(const string &s, char c) {
	vector<string> v; stringstream ss(s); string x;
	while (getline(ss, x, c)) v.push_back(x);
	return v;
}
#define DEBUG(args...) { vector<string> _v = split(#args, ','); err(_v.begin(), args); }
void err(vector<string>::iterator it) {}
template<typename T, typename... Args>
void err(vector<string>::iterator it, T a, Args... args) {
	cerr << "[DEBUG] " << it -> substr((*it)[0] == ' ', it -> length()) << " = " << a << '\n';
	err(++it, args...);
}
 
typedef long long ll;
const int MOD = 1000000007;
 
template<class T, class U> inline T tmin(T a, U b) { return (a < b) ? a : b; }
template<class T, class U> inline T tmax(T a, U b) { return (a > b) ? a : b; }
template<class T, class U> inline void amax(T &a, U b) { if (b > a) a = b; }
template<class T, class U> inline void amin(T &a, U b) { if (b < a) a = b; }
template<class T> T gcd(T a, T b) { while (b != 0) { T c = a; a = b; b = c % b; } return a; }
 
#define in(x) int x; cin >> x
#define ou(x) cout << x << endl
 
int main(int argc, char *argv[]) {
  ios_base::sync_with_stdio(false);
  int n; cin >> n;
  vector<int> a(n);
  REPU(i, 0, n) {
    cin >> a[i];
  }
  ll ans = 1;
  vector<int> mp(n, 0);
  int rem = 3;
  REPU(i, 0, n) {
    mp[a[i]]++;
    if (mp[a[i]] > 3) {
      puts("0"); return 0;
    }
    if (a[i] == 0) {
      ans = ans * (rem--) % MOD;
      continue;
    }
    if (mp[a[i] - 1] == 0) {
      puts("0"); return 0;
    }
    ans = ans * mp[a[i] - 1] % MOD;
    mp[a[i] - 1]--;
    
  }
  cout << ans << endl;
  return 0;
}