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)

N = int(input())
ans = 1
*a, = map(int, input().split())
mod = 10**9+7

l = [[0,0,0] for _ in range(N+1)]
r, g, b = 0, 0, 0

for i, j in enumerate(a):
    if i:
        if j==0:
            if g==0:
                g += 1
            else:
                b += 1
        else:
            if r==j:
                r += 1
            elif g==j:
                g += 1
            elif b==j:
                b += 1
    else:
        r += 1
     
    l[i+1][0] = r
    l[i+1][1] = g
    l[i+1][2] = b

ans = 1
for i,j in zip(a, l):
    ans *= j.count(i)
    ans %= mod

print(ans)