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.

Examples

Input

6
0 1 2 3 4 5


Output

3


Input

3
0 0 0


Output

6


Input

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


Output

115295190
	import java.util.*;
	import java.util.Map.Entry;
	 
	 
	 class Main {
		 static int mod =  (int) (Math.pow(10,9)+7);
//		 static int mod =  (int) 998244353;
		 static List<ArrayList<Integer>>  list = new ArrayList<ArrayList<Integer>>();
	    public static void main(String[] args) {
	    	
	        Scanner sc = new Scanner(System.in);
	        int N = sc.nextInt();	
	        long[] a = new long[N];
	        for (int i=0 ; i<N; i++) {
	            a[i] = Long.parseLong(sc.next());
	        }
	        long ans=1;
	        int[] m = new int[3];
	        for(int i=0;i<N;i++) {
	        	int tmp =0;
	        	for(int j=0;j<3;j++) {
	        		if(m[j]==a[i])tmp++;
	        	}
	        	for(int j=0;j<3;j++) {
	        		if(m[j]==a[i]) {
	        			m[j]++;
	        			break;
	        		}
	        	}
	        	ans=(ans*tmp)%mod;
	        }
	        
	        
	        System.out.println(ans);
	        

	    }
	    
	    

	}