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 <bits/stdc++.h>
#define int long long
#define fastio ios_base::sync_with_stdio(false);cin.tie(0);cout.tie(0);
#define MAXN 100100
#define pb push_back
using namespace std;


// 0 1 2 ... x representa uma cor APENAS
// quantas sequencias possiveis?

int cnt[100000+100];

const int M = 1e9+7;
int32_t main(){
	fastio;
	int n;
    cin>>n;
    vector<int> v(n);
	cnt[0] = 3;
	
	int ans = 1;
	for(int i=0;i<n;i++){
		cin>>v[i];
		v[i]++;
		ans = (ans*cnt[v[i]-1])%M;
		cnt[v[i]-1]--;
		cnt[v[i]]++;
	}
	cout<<ans<<endl;
}