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: Accepted)

N = int(input())
A = list(map(int, input().split()))

mod = 1000000007

RGB = [1,0,0]
n_cols = 1
ans = 1

dp=[0]*(N+1)

#A[0]による初期条件
dp[0]=2
dp[1]=1

if A[0]>0:
  print(0)
  exit()
  
for a in A[1:]:
  if a==0:
    n_cols += 1
    dp[0]-=1
    dp[1]+=1
    if n_cols ==4:
      print(0)
      exit()
      
  else:
    if dp[a]==0:
      print(0)
      exit()
    else:
      ans *= dp[a]
      ans %= mod
      dp[a]-=1
      dp[a+1]+=1
      
if n_cols==1:
  ans *= 3
else:
  ans *= 6
ans %=mod
print(ans)