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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include<stdio.h>
#include<stdlib.h>


int main(void){


	long long int n;
	long long int a[100001];
	long long int i,j;
	long long int b;

	long long int ret;

	long long int c[3]={};

	long long int mod;

	mod = 1000000007;

	scanf("%lld",&n);

	//R,G,Bいずれかの色

	for(i=0;i<n;i++){
		scanf("%lld",&a[i]);
	}

//	c[0] = 1;
	ret = 1;

	for(i=0;i<n;i++){

		b = 0;

		for(j=0;j<3;j++){
			if(c[j] == a[i]){
				if(b == 0){ c[j]++;	}
				b++;
			}
		}

		ret = ( ret * b ) % mod;
//		printf("n:%d %d(b=%d)\n",i,ret,b);

	}

	printf("%lld\n",ret);


	return 0;
}