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++ (GCC 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep(i, n) for (int i = 0; i < (n); i++)
#define irep(i, n) for (int i = (n); i >= 0; i--)
using namespace std;
using ll = long long;
using P = pair<int, int>;
const int INF = 1 << 25;
const int MOD = 1e9+7;
int a[100010];
int c[3];
int main() {
	int n;
	cin >> n;
	rep(i,n) cin >> a[i];

	ll ans = 1;
	rep(i,n) {
		int cnt = 0, id = -1;
		if (a[i] == c[0]) {
			cnt++; id = 0;
		}
		if (a[i] == c[1]) {
			cnt++; id = 1;
		}
		if (a[i] == c[2]) {
			cnt++; id = 2;
		}
		
		if (id == -1) {
			cout << 0 << endl;
			return 0;
		}
		c[id]++;
		ans *= cnt;
		ans %= MOD;
	}
	cout << ans << endl;
	return 0;
}