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 <cstdio>
using namespace std;
int n;
int arr[100005];
int c[100005];

const long long mod=1000000007;
int main(){
    scanf("%d",&n);
    for (int x=0;x<n;x++) scanf("%d",&arr[x]);
    
    for (int x=0;x<n;x++) {
        if (arr[x]!=x) goto _notsped;
    }
    
    printf("3\n");
    return 0;
    
    _notsped:;
    
    c[0]=3;
    for (int x=0;x<n;x++) arr[x]++;
    
    long long ans=1;
    
    for (int x=0;x<n;x++){
        c[arr[x]]++;
        if (arr[x]){
            ans=(ans*c[arr[x]-1])%mod;
            c[arr[x]-1]--;
        }
    }
    printf("%lld\n",ans);
}