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 "bits/stdc++.h"
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < n; i++)
#define repr(i, n) for (int i = n - 1; i >= 0; i--)

const int inf = 1000000007;
const int MOD = 1000000007;
const long long INF = 1000000000000000007;

int N;
int A[101010];
int num[101010][3];
ll ans = 1;

int main()
{
    cin >> N;
    rep(i, N)
    {
        cin >> A[i + 1];
        bool flag = true;
        int var = 0;
        for (int j = 0; j < 3; j++)
        {
            if (num[i][j] == A[i + 1])
            {
                var++;
            }
            if (flag && num[i][j] == A[i + 1])
            {
                num[i + 1][j] = num[i][j] + 1;
                flag = false;
            }
            else
            {
                num[i + 1][j] = num[i][j];
            }
        }
        ans = ans * var % MOD;
    }

    cout << ans << endl;
}