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)

import sys

read = sys.stdin.buffer.read
input = sys.stdin.buffer.readline
inputs = sys.stdin.buffer.readlines


# rstrip().decode('utf-8')
# INF=float("inf")
MOD=10**9+7
# sys.setrecursionlimit(2147483647)
# import math
#import numpy as np
# import operator
import bisect
# from heapq import heapify,heappop,heappush
#from math import gcd
# from fractions import gcd
#from collections import deque
#from collections import defaultdict
# from collections import Counter
#from itertools import accumulate
# from itertools import groupby
# from itertools import permutations
# from itertools import combinations
# from scipy.sparse import csr_matrix
# from scipy.sparse.csgraph import floyd_warshall
# from scipy.sparse.csgraph import csgraph_from_dense
# from scipy.sparse.csgraph import dijkstra
# map(int,input().split())


def main():
	n,*a=map(int,read().split())
	
	aa=max(a)
	
	li=[[] for _ in range(aa+1)]
	
	for i in range(n):
		li[a[i]].append(i)
	
	if len(li[0])>3 or len(li[0])==0:
		print(0)
		exit(0)
	else:
		ans=3 if len(li[0])==1 else 6
	for i in range(1,aa+1):
		if len(li[i])>3 or len(li[i])==0 or len(li[i])>len(li[i-1]):
			print(0)
			exit(0)
		else:
			k=bisect.bisect_right(li[i-1],li[i][0])
			ans*=k
			ans%=MOD
			
			if len(li[i])>1:
				k=bisect.bisect_right(li[i-1],li[i][1])-1
				ans *= k
				ans %= MOD
		
	print(ans)
	
	
if __name__ == "__main__":
		main()