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: Wrong Answer)

# coding: utf-8
MOD = 1000000007
num = int(input())
says = list(map(int, input().split()))

ans = 0
colors = 0
sets = [0, 0, 0]
for i in range(num):
    if colors == 0:
        sets[0] += 1
        colors += 1
        ans = 3
    elif colors == 1:
        if says[i] == 0:
            sets[1] += 1
            colors += 1
            ans *= 2
        else:
            sets[0] += 1
    elif colors == 2:
        if says[i] == 0:
            sets[2] += 1
            colors += 1
        else:
            if sets[0] == says[i]:
                sets[0] += 1
                if sets[1] == says[i]:
                    ans *= 2
            elif sets[1] == says[i]:
                sets[1] += 1
            else:
                ans = 0
                break
    elif colors == 3:
        if sets[0] == says[i]:
            sets[0] += 1
            if sets[1] == says[i] and sets[2] == says[i]:
                ans *= 3
            elif sets[1] == says[i] or sets[2] == says[i]:
                ans *= 2
        elif sets[1] == says[i]:
            sets[1] += 1
            if sets[2] == says[i]:
                ans *= 2
        elif sets[2] == says[i]:
            sets[2] += 1
        else:
            ans = 0
            break
#print(sets)
print(ans % MOD)