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 Go (1.14.1) (judge verdict: Wrong Answer)

package main

import "fmt"

func main() {
	var N int
	fmt.Scanf("%v", &N)
	A := make([]int, N)
	for i := 0; i < N; i++ {
		fmt.Scanf("%v", &A[i])
	}

	numR := 0
	numG := 0
	numB := 0

	// 最初の一人はRとする
	numR = 1
	var pat uint64 = 3
	for i := 1; i < N; i++ {
		cand := 0
		var candp *int
		if A[i] == numR {
			cand++
			candp = &numR
		}
		if A[i] == numG {
			cand++
			candp = &numG
		}
		if A[i] == numB {
			cand++
			candp = &numB
		}
		if cand == 0 {
			fmt.Printf("0\n")
			return
		}
		//fmt.Printf("cand=%v\n", cand)
		pat *= uint64(cand)
		*candp++
	}

	fmt.Printf("%v\n", pat%1000000007)

}