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 Fortran (GNU Fortran 9.2.1) (judge verdict: Wrong Answer)

program main
    use,intrinsic :: iso_fortran_env
    implicit none
    integer(int64):: i,n,ans=1
    integer(int64),parameter:: md = 1000000007
    integer(int64), allocatable:: a(:)

    read*, n
    allocate(a(n))
    read*, a(:)

    block; integer:: i1=0, i2=0, i3=0
        do i=1,n
            if (i1 == i2 .and. i2 == i3) then
                ans=mod(ans*3, md)
                i1=i1+1
            else if (i1 == i2 .and. a(i) == i1) then
                ans=mod(ans*2, md)
                i1=i1+1
            else if (i2 == i3 .and. a(i) == i2) then
                ans=mod(ans*2, md)
                i2=i2+1
            else
                if (a(i) == i1) then
                    i1=i1+1
                else if(a(i) == i2) then
                    i2=i2+1
                else if (a(i) == i3) then
                    i3=i3+1
                else
                    print'(i0)', 0
                    stop
                end if
            end if
        end do
    end block
    print'(i0)', ans
end program main