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>

#ifdef _DEBUG
#define debug(x) cerr << "line: " << __LINE__ << ", func: " << __func__ << " ->  " << #x << " = " << x << endl
#else
#define debug(x)
#endif

#define all(s) begin(s), end(s)
#define rall(s) rbegin(s), rend(s)
#define rep(i, a, b) for (int i = (a); i < (b); i++)
#define rrep(i, a, b) for (int i = ((a)-1); i >= (b); i--)
#define pb push_back
#define sz(a) int((a).size())
#define put(a) ((cout) << (a) << (endl))
#define putf(a, n) ((cout) << (fixed) << (setprecision(n)) << (a) << (endl))
#define deg2rad(x) (((x)*PI) / (180.0))
#define rad2deg(x) (((x) * (180.0)) / PI)

using namespace std;

using ll = long long;
using ull = unsigned long long;
using i_i = pair<int, int>;
using ll_ll = pair<ll, ll>;
using d_ll = pair<double, ll>;
using ll_d = pair<ll, double>;
using d_d = pair<double, double>;

static constexpr ll LL_INF = 1LL << 60;
static constexpr int I_INF = 1 << 28;
static constexpr double PI = static_cast<double>(3.14159265358979323846264338327950288);
static constexpr double EPS = numeric_limits<double>::epsilon();
static constexpr ll MOD = 1000000007;

static map<type_index, const char* const> scanType = {
    {typeid(int), "%d"}, {typeid(ll), "%lld"}, {typeid(double), "%lf"}, {typeid(char), "%c"}};

template <class T> static void scan(vector<T>& v);
[[maybe_unused]] static void scan(vector<string>& v, bool isWord = true);
template <class T> static inline bool chmax(T& a, T b);
template <class T> static inline bool chmin(T& a, T b);
template <class T> static inline T gcd(T a, T b);
template <class T> static inline T lcm(T a, T b);
template <class A, size_t N, class T> static void Fill(A (&arr)[N], const T& val);
template <class T> T mod(T a, T m);

int main(int argc, char* argv[]) {
  long long N;
  scanf("%lld", &N);
  std::vector<long long> A(N);
  for (int i = 0; i < N; i++) {
    scanf("%lld", &A[i]);
  }

  vector<ll> count(3);
  ll ans = 1;
  for (ll c : A) {
    int mul = 0, index = -1;
    rep(i, 0, 3) {
      if (count[i] != c) continue;
      mul++;
      index = i;
    }

    if (index == -1) {
      put(0);
      return 0;
    }

    count[index]++;
    ans = mod(ans * mul, MOD);
  }

  put(ans);
  return 0;
}

template <class T> static void scan(vector<T>& v) {
  auto tFormat = scanType[typeid(T)];
  for (T& n : v) {
    scanf(tFormat, &n);
  }
}

static void scan(vector<string>& v, bool isWord) {
  if (isWord) {
    for (auto& n : v) {
      cin >> n;
    }
    return;
  }

  int i = 0, size = v.size();
  string s;
  getline(cin, s);

  if (s.size() != 0) {
    i++;
    v[0] = s;
  }

  for (; i < size; ++i) {
    getline(cin, v[i]);
  }
}

template <class T> inline bool chmax(T& a, T b) {
  if (a < b) {
    a = b;
    return 1;
  }
  return 0;
}

template <class T> inline bool chmin(T& a, T b) {
  if (a > b) {
    a = b;
    return 1;
  }
  return 0;
}

template <class T> inline T gcd(T a, T b) { return __gcd(a, b); }

template <class T> inline T lcm(T a, T b) { return (a * b) / gcd(a, b); }

template <class A, size_t N, class T> void Fill(A (&arr)[N], const T& val) {
  std::fill((T*)arr, (T*)(arr + N), val);
}

template <class T> T mod(T a, T m) { return (a % m + m) % m; }