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 Julia (0.5.0) (judge verdict: Accepted)

parseInt(x) = parse(Int, x)
parseMap(x::Array{SubString{String},1}) = map(parseInt, x)

function main()
	mod = 10^9+7
	n = readline() |> parseInt
	a = readline() |> split |> parseMap
	if a[1] != 0
		println(0)
	else
	dp = zeros(Int,n)
	dp[1] = 1
	r = 1
	g = 0
	b = 0
	for i in 2:n
		k = 0
		f = 0
		if a[i]==r
			r += 1
			f = 1
			k += 1
		end
		if a[i]==g
			if f == 0
				g += 1
				f += 1
			end
			k += 1
		end
		if a[i]==b
			if f == 0
				b += 1
				f += 1
			end
			k += 1
		end
		dp[i] = (dp[i-1]*k)%mod
	end
	dp[n] = (dp[n]*3)%mod
	println(dp[n])
end
end

main()