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>


using namespace std;
typedef long long ll;
#define REP(i,n) for(int i=0; i<int(n); i++)
#define FOR(i,m,n) for(int i=int(m); i<int(n); i++)
#define ALL(obj) (obj).begin(),(obj).end()
#define VI vector<int>
#define VLL vector<long long>
#define VVI vector<vector<int>>
#define VVLL vector<vector<long long>>
#define VC vector<char>
#define VS vector<string>
#define VVC vector<vector<char>>
#define VB vector<bool>
#define VVB vector<vector<bool>>
#define fore(i,a) for(auto &i:a)
typedef pair <int, int> P;
template<class T> bool chmax(T &a, T b) { if (a < b) { a = b; return true; } return false; }
template<class T> bool chmin(T &a, T b) { if (a > b) { a = b; return true; } return false; }
template<typename T> using min_priority_queue = priority_queue<T, vector<T>, greater<T>>;

const int  INF = 1 << 29;
const ll INFL = 1LL << 60;
const ll mod = 1000000007;




int main() {

	ll n;
	cin >> n;
	VLL dp(100005, 0);
	dp[0] = 3;
	VLL b(100005, 0);
	b[0]++;

	VI a(n);
	cin >> a[0];
	FOR(i,1, n) {
		cin >> a[i];
		if (a[i] == 0) {
			dp[i] += dp[i - 1];
		}
		else {
			dp[i] += (ll)(dp[i - 1] * (ll)(b[a[i] - 1] - b[a[i]])) % mod;
		}
		b[a[i]]++;
	}
	if (b[0] > 1)dp[n - 1] *= 2;
	dp[n - 1] %= mod;
	cout << dp[n - 1] << endl;
}