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: Runtime Error)

#include <iostream>
#include <vector>
using namespace std;

const long long MOD = 1000000007;

int main() {
    int N;
    cin >> N;
    vector<int> A(N);
    for (int i = 0; i < N; i++)
        cin >> A[i];

    long long res = 1;
    vector<int> C(3);
    for (int i = 0; i < N; i++) {
        long long cnt = 0, id = -1;
        if (A[i] == C[0]) { cnt++; id = 0; }
        if (A[i] == C[1]) { cnt++; id = 1; }
        if (A[i] == C[2]) { cnt++; id = 2; }

        res *= cnt;
        res %= MOD;
        C[id]++;
    }

    cout << res << endl;
    return 0;
}