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 REPP(i,a,b,c) for(int i=a; i<=b; i+=c)
#define REP(i,a,b) REPP(i,a,b,1)
#define REVV(i,a,b,c) for(int i=a; i>=b; i-=c)
#define REV(i,a,b) REVV(i,a,b,1)
#define FOR(i,a) REP(i,0,(int)a-1)
#define FORD(i,a) REV(i,(int)a-1,0)
#define PB push_back
#define POB pop_back
#define FI first
#define SE second
#define MP make_pair
typedef long long ll;
typedef unsigned long long ull;
typedef pair < int , int > pii;
typedef vector < int > vi;
typedef vector < pii > vii;
typedef vector < ll > vl;
typedef pair < ll , ll > pll;

const double PI = acos(-1);
const double EPS = 1e-9;
const ll MOD = 1e9 + 7;
const int INF = 1e9;
	

ll addMod(ll a, ll b){
	if(a + b >= MOD) return a + b - MOD;
	return a + b;
}

ll mulMod(ll a, ll b){
	return (a*b)%MOD;
}

ll fast(ll a, ll b){
	if(b == 0) return 1;
	ll tmp = fast(a,b/2);
	tmp = mulMod(tmp,tmp);
	if(b%2 == 1) tmp = mulMod(tmp,a);
	return tmp;
}

ll GCD(ll a, ll b){
	if(a > b) return GCD(b,a);
	if(a == 0) return b;
	return GCD(b%a,a);
}

#define getc getchar
template<typename T>
T getnum(){
	int sign = 1;
	T ret = 0;
	char c;

	do{
		c = getc();
	}while(c == ' ' || c == '\n');
	if(c == '-')sign = -1;
	else ret = c-'0';
	while(1){
		c = getc();
		if(c < '0' || c > '9')break;
		ret = 10*ret + c-'0';
	}
	return sign * ret;
}

inline void ini(int& x){
	x = getnum<int>();
}

//////////////////////////////////////////////

const int N = 1e5;

int arr[N + 5];
int cnt[N + 5];

int main(){
	ios_base :: sync_with_stdio(0); cin.tie(0); cout.tie(0);
	int n; cin >> n;
	REP(i,1,n) cin >> arr[i];
	ll ans = 1;
	int cnt0 = 0;
	REP(i,1,n){
		if(arr[i] > 0){
			ans = mulMod(ans,cnt[arr[i]-1]);
			cnt[arr[i]-1]--;
		}
		else ans = mulMod(ans,3-cnt0), cnt0++;
		cnt[arr[i]]++;
	}
	cout << ans << endl;
	return 0;
}