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>
#define N (int) (1e5 + 10)
#define MOD (int) (1e9 + 7)

int main() {
    std::ios_base::sync_with_stdio(false);
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);

#if DEBUG_ON
    freopen("input", "r", stdin);
#endif

    int n, arr[N] = { 0 }, colors[3] = { 0 };
    std::cin >> n;
    for (int i = 0; i < n; ++i) {
        int a;
        std::cin >> a;
        bool added = false;
        for (int j = 0; j < 3; ++j) {
            if (a == colors[j]) {
                ++arr[i];
                if (!added) {
                    ++colors[j];
                    added = true;
                }
            }
        }
    }
    long long res = 1;
    for (int i = 0; i < n; ++i) {
        res *= arr[i];
        res %= MOD;
    }
    std::cout << res << '\n';
    return 0;
}