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: Wrong Answer)

#include<iostream>
#include<cmath>
#include<algorithm>
#include<vector>
#include<queue>

using namespace std;

int main(){

  long long m=1000000007;
  long long int r=0,b=0,g=0;//それぞれ赤、青、緑の帽子の数

  int n;
  cin >> n;

  long long int l=1;

  //0人目は必ず0と言う
  long long a;
  cin >>a;
  r++;
  l*=3;
  for(int i=1;i<n;i++){
    cin >> a;
    //i人目の色としてあり得る色の数をlにかけていく
    if(r==a){
      if(b==a){
        if(g==a){
          l*=3;
          l%=m;
          r++;
        }
        else{
          l*=2;
          l%=m;
          b++;
        }
      }
      else{
        if(g==a){
          l*=2;
          l%=m;
          r++;
        }
        else{
          r++;
        }
      }
    }
    else{
      if(b==a){
        if(g==a){
          l*=2;
          l%=m;
          b++;
        }
        else{
          b++;
        }
      }
      else{
        if(g==a){
          g++;
        }
      }
    }
  }

  cout << l << endl;
}