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 <iostream>
#include <cassert>
using namespace std;
const int MOD = 1e9 + 7;
int N, A[101010], occ[101010];
int main(){
	cin >> N;
	for(int i = 0; i < N; i++)cin >> A[i];

	int cnt_ch = 0;
	long long int res = 1;
	
	for(int i = 0; i < N; i++){
		if(A[i] != 0){
			res = res * occ[A[i] - 1];
			res = res % MOD;
			
			if(occ[A[i] - 1] <= 0)return cout << 0 << '\n', 0;
			occ[A[i] - 1]--;
		}
		else cnt_ch++;

		if(cnt_ch > 3)return cout << 0 << '\n', 0;
		occ[A[i]]++;
	}
	res = res * (cnt_ch == 1 ? 3 : 6);
	res = res % MOD;

	cout << res << '\n';
}