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 <bits/stdc++.h>
#define rep(i, n) for(int i = 0; i < n; i++)
#define INF 1e18
using namespace std;
typedef long long ll;
int main(){
    ll n;
    vector<ll> a(n);
    cin>>n;
    rep(i,n) cin>>a[i];
    ll x=0,y=0,z=0;
    ll ans=1;
    rep(i,n){
        ll cnt=0;
        bool flag=true;
        if (x==a[i]){
            ++cnt;
            x=cnt;
            flag=false;
        } 
        if (y==a[i]){
            ++cnt;
            if (flag){
                y=cnt;
                flag=false;
            }
        }
        if (z==a[i]){
            ++cnt;
            if (flag){
                z=cnt;
                flag=false;
            }
        }
        ans*=cnt;
    }
    cout<<ans<<endl;
}