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: Wrong Answer)

#include <iostream>
#include <algorithm>
using namespace std;
typedef long long ll;


int main(void) {
	int n, i, a[100003], s[100003] = {}, t = 0;
	ll ans = 1;
	const int mod = 1e9 + 7;

	cin >> n;
	for (i = 0; i < n; i++) {
		cin >> a[i];
	}

	for (i = 0; i < n; i++) {
		if (a[i] > 0) {
			ans = ans * s[a[i] - 1] % mod;
			s[a[i] - 1]--;
		}
		else {
			t++;
		}
		s[a[i]]++;
		if (s[a[i]] > 3) {
			cout << 0 << endl;
			return 0;
		}
	}

	if (t == 3) ans = ans * 6 % mod;
	if (t == 2) ans = ans * 2 % mod;

	cout << ans << endl;

	return 0;
}