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: Wrong Answer)

#include <bits/stdc++.h>
#define FOR(i,a,b) for(ll i=(a);i<(b);++i)
#define rep(i,n) FOR(i,0,n)
#define all(x) (x).begin(),(x).end()
#define PRINT(V) cout << V << "\n"
#define SORT(V) sort((V).begin(),(V).end())
#define RSORT(V) sort((V).rbegin(), (V).rend())
using namespace std;
using ll = long long;
template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
const ll INF = 1e13;
typedef pair<ll,ll> P;
int dp[100001];
int main(){
    int n;
    cin >> n;
    int a[100001];
    rep(i,n){
        cin >> a[i];
    }
    ll color[3] = {0};
    ll ans = 1;
    ll c;
    ll check = 0;
    rep(i,n){
        if (i == 0){
            color[0]++;
            ans *= 3;
            continue;
        }
        rep(j,3){
            if (a[i] == color[j]){
                check++;
                c = j;
            }
        }
        if (check == 0){
            ans = 0;
            break;
        }
        ans *= check;
        ans %= 1000000007;
        color[c]++;
        check = 0;
    }
    c = 0;
    rep(i,3){
        if (color[i] != 0) c++;
    }
    PRINT(ans);
}