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 Python (3.4.3) (judge verdict: Runtime Error)

# def i():
#     yield "100000"
#     a = 0
#     b = 0
#     c = 0
#     l = []
#     for i in range(100000):
#         import random
#         r = random.randint(0, 2)
#         if r == 0:
#             l.append(str(a))
#             a += 1
#         elif r == 1:
#             l.append(str(b))
#             b += 1
#         else:
#             l.append(str(c))
#             c += 1
#     yield " ".join(l)
# input = i().__next__
def main():
    N = int(input())
    A = [int(i) for i in input().split()]
    cur = 1
    nums = []
    for i in range(N):
        if A[i] == 0:
            cur *= 1
            nums.append(0)
            continue
        #A[i] != 0
        cnt = 0
        for j, n in enumerate(nums):
            if n == A[i] - 1:
                if cnt == 0:
                    nums[j] += 1
                cnt += 1
        cur *= cnt
        cur %= 10**9+7
        # print(nums)
    m = [0, 3, 6, 6]
    
    print((cur * m[len(nums)]) % (10**9+7))
main()