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 main(void) {
    long long N, A[100005], B[10], X, K, i, j;
    scanf("%lld", &N);
    for (i=1; i<=N; i++) scanf("%lld", &A[i]);
    for (i=1; i<=3; i++) B[i]=0;
    X=1;
    for (i=1; i<=N; i++) {
        K=0;
        for (j=1; j<=3; j++) {
            if (B[j]==A[i]) {
                if (K==0) B[j]++;
                K++;
            }
        }
        if (K==3) X*=3;
        else if (K==2) X*=2;
        X%=1000000007;
        // printf("%d: %d\n", i, X);
    }
    // printf("%lld %lld %lld\n", B[1], B[2], B[3]);
    printf("%lld", X); 
    return 0;
}