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>
#define fi first
#define se second
#define rep(i,n) for(int i = 0; i < (n); ++i)
#define drep(i,n) for(int i = (n)-1; i >= 0; --i)
#define srep(i,s,t) for (int i = s; i < t; ++i)
#define rng(a) a.begin(),a.end()
#define sz(x) (int)(x).size()
#define uni(x) x.erase(unique(rng(x)),x.end())
#define show(x) cout<<#x<<" = "<<x<<endl;
#define PQ(T) priority_queue<T,v(T),greater<T> >
#define newline puts("")
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
typedef long long int ll;
typedef pair<int,int> P;
typedef set<int> S;
typedef queue<int> Q;
typedef queue<P> QP;
typedef vector<int> vi;
typedef vector<vi> vvi;
typedef vector<ll> vl;
typedef vector<P> vp;
const ll LINF = 1001002003004005006ll;
const int INF = 1001001001;
const int MOD = 1000000007;
  
int main() {
  int N;
  cin >> N;
  vi A(N);
  rep(i,N) {
    cin >> A[i];
  }
  if(N==1) {
    if(A[0] == 0) {
      cout << 3 << endl;
    } else {
      cout << 0 << endl;
    }
    return 0;
  }
  if(A[0] != 0) {
    cout << 0 << endl;
    return 0;
  }
  vl rgb(3,0);
  rgb[0] = 1;
  ll ans = 3;
  srep(i,1,N) {
    ll cnt = 0;
    int k = -1;
    rep(j,3) {
      if(A[i] == rgb[j]) {
        cnt++;
        k = j;
      }
    }
    if(cnt == 0) {
      cout << 0 << endl;
      return 0;
    }
    ans *= cnt;
    ans %= MOD;
    rgb[k]++;
  }
  cout << ans << endl;
  return 0;
}