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 rep(i,n) for(int i=0; i<(n); i++)
#define reps(i,s,n) for(int i=(s); i<(n); i++)
#define all(v) v.begin(),v.end()
#define res(n) resize(n)
#define rev(v) reverse(v.begin(),v.end())
#define so(v) sort(v.begin(),v.end())
#define outve(v) for(auto i : v) cout << i << " ";cout << endl
#define in(n,v) for(int i=0; i<(n); i++){cin >> v[i];}
#define out(n) cout << (n) << endl
#define fi first
#define se second
#define ve vector
#define pa pair
using namespace std;
typedef long long ll;
typedef vector<int> vi;
typedef vector<vector<int>> vvi;
typedef vector<ll> vl;
typedef vector<vector<ll>> vvl;
typedef vector<string> vs;
typedef vector<vector<int>> vvi;
typedef vector<pair<int,int>> vpi;
typedef vector<pair<ll,ll>> vpl;
typedef vector<vector<pair<int,int>>> vvp;


const ll mod = 1000000007;


int main()
{
    int N;
    cin >> N;
    vl A(N);
    in(N,A);
    
    vl B(100009,0);
    ll ans = 1;
    
    rep(i,N){
        if(A[i] == 0){
            ans *= (3-B[A[i]]);
            ans %= mod;
            B[A[i]]++;
        }else{
            ans *= (B[A[i]-1]-B[A[i]]);
            ans %= mod;
            B[A[i]]++;
        }
        
    }
    out(ans);
    
    
    return 0;
}