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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int A[100000];

void Do(int N){
  int i, a[3], j, S, c, C;
  for(i = 0;i < N;i++) scanf("%d", &A[i]);
  a[0] = a[1] = a[2] = 0;
  S = 1;
  for(i = 0;i < N;i++){
    c = C = 0;
    for(j = 0;j < 3;j++){
      if(A[i] == a[j]){
	c++;
	if(C == 0){
	  a[j]++;
	  C = 1;
	}
      }
    }
    S *= c;
    S %= 1000000007;
    if(S == 0) break;
  }
  printf("%d\n", S);
}

int main(void){
  int N;
  scanf("%d", &N);
  Do(N);
  return 0;
}