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 PyPy3 (2.4.0) (judge verdict: Accepted)

inpl = lambda: list(map(int,input().split()))
MOD = 10**9+7
N = int(input())
A = inpl()
ans = 1
nc = [0] * 3
for i in range(N):
    k = 0
    a = A[i]
    while nc[k] > a:
        k += 1
        if k > 2:
            print(0)
            exit()
    if nc[k] < a:
        print(0)
        exit()
    if k <= 1 and nc[k+1] == a:
        s = 2
        if k == 0 and nc[k+2] == a:
            s = 3
        ans = ans * s % MOD
    nc[k] += 1
print(ans)