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>
using namespace std;
 
#define IOS ios::sync_with_stdio(0); cin.tie(0); cout.tie(0);
#define endl "\n"
#define int long long

const int N = 1e5 + 5;
const int MOD = 1e9 + 7;

int pow(int a, int b, int m)
{
	int ans=1;
	while(b)
	{
		if(b&1)
			ans=(ans*a)%m;
		b/=2;
		a=(a*a)%m;
	}
	return ans;
}

int n;
int a[N], cnt[N];

int32_t main()
{
	IOS;
	cin >> n;
	for(int i = 1; i <= n; i++)
		cin >> a[i];
	int ans = 1;
	for(int i = 1; i <= n; i++)
	{
		if(a[i] == 0)
		{
			if(cnt[0] == 0)
				ans *= 3;
			else if(cnt[0] == 1)
				ans *= 2;
		}
		else
		{
			if(cnt[a[i] - 1] - cnt[a[i]] <= 0)
			{
				cout << 0;
				return 0;
			}
			ans *= (cnt[a[i] - 1] - cnt[a[i]]);
		}
		ans %= MOD;
		cnt[a[i]]++;
	}
	for(int i = 0; i < n; i++)
	{
		if(cnt[i] > 3)
		{
			cout << 0;
			return 0;
		}
	}
	cout << ans;
	return 0;
}