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 (GCC 9.2.1) (judge verdict: Accepted)

#include <stdio.h>

int main(void){
    int n;
    int a[100000];
    scanf("%d", &n);
    int i, j, k;
    for(i = 0; i < n; i++){
        scanf("%d", &a[i]);
    }

    long long int ans = 1;
    long long int mod = 1000000007;
    int co[] = {0, 0, 0};
    long long int cnt;
    //とりあえず，先頭の1人を赤，次の人を青と仮定して計算し，後で6倍する
    for(i = 0; i < n; i++){
        cnt = 0;
        for(j = 0; j < 3; j++){
            if(co[j] == a[i]){
                if(cnt == 0){
                    co[j]++;
                }
                cnt++;
            }
        }
        ans *= cnt;
        ans %= mod;
    }
    printf("%lld\n", ans);
    return 0;
}