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 (3.8.2) (judge verdict: Wrong Answer)

import sys,math,collections,itertools
input = sys.stdin.readline

N=int(input())
A=list(map(int,input().split()))
color1 = -1
color2 = -1
color3 = -1

m = 10**9+7
patern = 1

for a in A:
    if color1 == a-1 and color2 == a-1 and color3 == a-1:
        patern = (patern * 3)%m
        color1 = a
    elif (color1 != a-1 and color2 == a-1 and color3 == a-1):
        patern = (patern * 2)%m
        color2 = a

    elif (color1 == a-1 and color2 == a-1 and color3 != a-1):
        patern = (patern * 2)%m
        color1 = a
    elif (color1 == a-1 and color2 != a-1 and color3 != a-1):
        color1 = a

    elif (color1 != a-1 and color2 == a-1 and color3 != a-1):
        color2 = a

    elif (color1 != a-1 and color2 != a-1 and color3 == a-1):
        color3 = a
    
print(patern)