#include <bits/stdc++.h>
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  ~debug() { cerr << endl; }
  template <class c>
  typename enable_if<sizeof dud<c>(0) != 1, debug&>::type operator<<(c i) {
    cerr << boolalpha << i;
    return *this;
  }
  template <class c>
  typename enable_if<sizeof dud<c>(0) == 1, debug&>::type operator<<(c i) {
    return *this << range(begin(i), end(i));
  }
  template <class c, class b>
  debug& operator<<(pair<b, c> d) {
    return *this << "(" << d.first << ", " << d.second << ")";
  }
  template <class c>
  debug& operator<<(rge<c> d) {
    *this << "[";
    for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it;
    return *this << "]";
  }
};
long double eps = (long double)1 / 1e6;
const long double pi = 3.14159265359;
long long inf = 2e9, mod1 = 1e9 + 7;
long long sqr(long long a) { return a * a; }
long long qb(long long a) { return a * a * a; }
template <typename T>
bool umax(T& a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <typename T>
bool umin(T& a, T b) {
  return b < a ? a = b, 1 : 0;
}
bool is_prime(long long val) {
  for (long long i = 2; i <= sqrt(val); i++)
    if (val % i == 0) return 0;
  return 1;
}
long long gcd(long long a, long long b) { return !a ? b : gcd(b % a, a); }
long long binpow(long long a, long long b, long long mod) {
  return b ? (b % 2 ? (a * (sqr(binpow(a, b / 2, mod)) % mod)) % mod
                    : sqr(binpow(a, b / 2, mod)) % mod)
           : 1;
}
long long binmult(long long a, long long b, long long mod) {
  return b ? (b % 2 ? (2 * binmult(a, b / 2, mod) + a) % mod
                    : (2 * binmult(a, b / 2, mod)) % mod)
           : 0;
}
const long long R = 1e4;
const long long tx[4] = {0, 0, -1, 1};
const long long ty[4] = {-1, 1, 0, 0};
const char rev_to[4] = {'E', 'W', 'N', 'S'};
const int M = 999999937;
const int NM = 1 << 14;
const int N = 3002;
const int ppp = 73;
const int Y = 1;
const int X = 0;
auto rnd = bind(uniform_int_distribution<long long>(1, 125), mt19937(time(0)));
void bad() {
  cout << "-1";
  exit(0);
}
pair<int, int> lol[17][N];
signed main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(0);
  ;
  int n;
  cin >> n;
  vector<pair<int, int> > a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i].first;
    a[i].second = i;
  }
  sort(a.begin(), a.end());
  vector<int> b(n - 1);
  for (int i = 0; i + 1 < n; i++) {
    b[i] = a[i + 1].first - a[i].first;
    lol[0][i] = make_pair(b[i], i);
  }
  int m = (int)b.size();
  for (int i = 1; i < 17; i++) {
    for (int j = 0; j < m; j++) {
      lol[i][j] = max(lol[i - 1][j], lol[i - 1][(j + (1ll << i - 1)) % m]);
    }
  }
  vector<int> pows(N);
  for (int i = 2; i < N; i++) {
    pows[i] = pows[i >> 1] + 1;
  }
  auto get = [&](int l, int r) {
    if (r < 0) return make_pair(0, -1);
    int pl = l;
    umax(l, 0);
    umin(r, m - 1);
    umax(r, 0);
    int lvl = pows[r - l + 1];
    pair<int, int> ans = max(lol[lvl][l], lol[lvl][r - (1ll << lvl) + 1]);
    if (pl < 0) umax(ans, make_pair(a[0].first, -1));
    return ans;
  };
  int first = n, second = n, t = n;
  pair<int, pair<int, int> > aaa = make_pair(-1, make_pair(-1, -1));
  for (int i = 0; i < m; i++) {
    for (int j = i + 1; j < m; j++) {
      int cnt3 = m - j;
      int cnt2 = j - i;
      int lcnt1 = max(ceil((long double)cnt3 / 2), ceil((long double)cnt2 / 2));
      int rcnt1 = min(cnt3 * 2, cnt2 * 2);
      if (min(cnt2, cnt3) * 2 < max(cnt2, cnt3)) continue;
      if (lcnt1 > i + 1) continue;
      umax(lcnt1, 1);
      pair<int, int> heh = get(i - rcnt1, i - lcnt1);
      pair<int, pair<int, int> > kek = {b[j], {b[i], heh.first}};
      if (kek > aaa) {
        aaa = kek;
        first = heh.second;
        second = i;
        t = j;
      }
    }
  }
  vector<int> ans(n, -1);
  for (int i = 0; i < n; i++) {
    assert(a[i].second < n);
    if (i > t)
      ans[a[i].second] = 1;
    else if (i > second)
      ans[a[i].second] = 2;
    else if (i > first)
      ans[a[i].second] = 3;
    else
      ans[a[i].second] = -1;
  }
  for (auto& z : ans) cout << z << ' ';
  return 0;
}

### Prompt

Create a solution in cpp for the following problem:

Alexey recently held a programming contest for students from Berland. n students participated in a contest, i-th of them solved ai problems. Now he wants to award some contestants. Alexey can award the students with diplomas of three different degrees. Each student either will receive one diploma of some degree, or won't receive any diplomas at all. Let cntx be the number of students that are awarded with diplomas of degree x (1 ≤ x ≤ 3). The following conditions must hold:

  * For each x (1 ≤ x ≤ 3) cntx > 0; 
  * For any two degrees x and y cntx ≤ 2·cnty. 



Of course, there are a lot of ways to distribute the diplomas. Let bi be the degree of diploma i-th student will receive (or  - 1 if i-th student won't receive any diplomas). Also for any x such that 1 ≤ x ≤ 3 let cx be the maximum number of problems solved by a student that receives a diploma of degree x, and dx be the minimum number of problems solved by a student that receives a diploma of degree x. Alexey wants to distribute the diplomas in such a way that:

  1. If student i solved more problems than student j, then he has to be awarded not worse than student j (it's impossible that student j receives a diploma and i doesn't receive any, and also it's impossible that both of them receive a diploma, but bj < bi); 
  2. d1 - c2 is maximum possible; 
  3. Among all ways that maximize the previous expression, d2 - c3 is maximum possible; 
  4. Among all ways that correspond to the two previous conditions, d3 - c - 1 is maximum possible, where c - 1 is the maximum number of problems solved by a student that doesn't receive any diploma (or 0 if each student is awarded with some diploma). 



Help Alexey to find a way to award the contestants!

Input

The first line contains one integer number n (3 ≤ n ≤ 3000).

The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 5000).

Output

Output n numbers. i-th number must be equal to the degree of diploma i-th contestant will receive (or  - 1 if he doesn't receive any diploma).

If there are multiple optimal solutions, print any of them. It is guaranteed that the answer always exists.

Examples

Input

4
1 2 3 4


Output

3 3 2 1 


Input

6
1 4 3 1 1 2


Output

-1 1 2 -1 -1 3 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <class c>
struct rge {
  c b, e;
};
template <class c>
rge<c> range(c i, c j) {
  return rge<c>{i, j};
}
template <class c>
auto dud(c* x) -> decltype(cerr << *x, 0);
template <class c>
char dud(...);
struct debug {
  ~debug() { cerr << endl; }
  template <class c>
  typename enable_if<sizeof dud<c>(0) != 1, debug&>::type operator<<(c i) {
    cerr << boolalpha << i;
    return *this;
  }
  template <class c>
  typename enable_if<sizeof dud<c>(0) == 1, debug&>::type operator<<(c i) {
    return *this << range(begin(i), end(i));
  }
  template <class c, class b>
  debug& operator<<(pair<b, c> d) {
    return *this << "(" << d.first << ", " << d.second << ")";
  }
  template <class c>
  debug& operator<<(rge<c> d) {
    *this << "[";
    for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it;
    return *this << "]";
  }
};
long double eps = (long double)1 / 1e6;
const long double pi = 3.14159265359;
long long inf = 2e9, mod1 = 1e9 + 7;
long long sqr(long long a) { return a * a; }
long long qb(long long a) { return a * a * a; }
template <typename T>
bool umax(T& a, T b) {
  return a < b ? a = b, 1 : 0;
}
template <typename T>
bool umin(T& a, T b) {
  return b < a ? a = b, 1 : 0;
}
bool is_prime(long long val) {
  for (long long i = 2; i <= sqrt(val); i++)
    if (val % i == 0) return 0;
  return 1;
}
long long gcd(long long a, long long b) { return !a ? b : gcd(b % a, a); }
long long binpow(long long a, long long b, long long mod) {
  return b ? (b % 2 ? (a * (sqr(binpow(a, b / 2, mod)) % mod)) % mod
                    : sqr(binpow(a, b / 2, mod)) % mod)
           : 1;
}
long long binmult(long long a, long long b, long long mod) {
  return b ? (b % 2 ? (2 * binmult(a, b / 2, mod) + a) % mod
                    : (2 * binmult(a, b / 2, mod)) % mod)
           : 0;
}
const long long R = 1e4;
const long long tx[4] = {0, 0, -1, 1};
const long long ty[4] = {-1, 1, 0, 0};
const char rev_to[4] = {'E', 'W', 'N', 'S'};
const int M = 999999937;
const int NM = 1 << 14;
const int N = 3002;
const int ppp = 73;
const int Y = 1;
const int X = 0;
auto rnd = bind(uniform_int_distribution<long long>(1, 125), mt19937(time(0)));
void bad() {
  cout << "-1";
  exit(0);
}
pair<int, int> lol[17][N];
signed main() {
  cin.tie(0);
  cout.tie(0);
  ios_base::sync_with_stdio(0);
  ;
  int n;
  cin >> n;
  vector<pair<int, int> > a(n);
  for (int i = 0; i < n; i++) {
    cin >> a[i].first;
    a[i].second = i;
  }
  sort(a.begin(), a.end());
  vector<int> b(n - 1);
  for (int i = 0; i + 1 < n; i++) {
    b[i] = a[i + 1].first - a[i].first;
    lol[0][i] = make_pair(b[i], i);
  }
  int m = (int)b.size();
  for (int i = 1; i < 17; i++) {
    for (int j = 0; j < m; j++) {
      lol[i][j] = max(lol[i - 1][j], lol[i - 1][(j + (1ll << i - 1)) % m]);
    }
  }
  vector<int> pows(N);
  for (int i = 2; i < N; i++) {
    pows[i] = pows[i >> 1] + 1;
  }
  auto get = [&](int l, int r) {
    if (r < 0) return make_pair(0, -1);
    int pl = l;
    umax(l, 0);
    umin(r, m - 1);
    umax(r, 0);
    int lvl = pows[r - l + 1];
    pair<int, int> ans = max(lol[lvl][l], lol[lvl][r - (1ll << lvl) + 1]);
    if (pl < 0) umax(ans, make_pair(a[0].first, -1));
    return ans;
  };
  int first = n, second = n, t = n;
  pair<int, pair<int, int> > aaa = make_pair(-1, make_pair(-1, -1));
  for (int i = 0; i < m; i++) {
    for (int j = i + 1; j < m; j++) {
      int cnt3 = m - j;
      int cnt2 = j - i;
      int lcnt1 = max(ceil((long double)cnt3 / 2), ceil((long double)cnt2 / 2));
      int rcnt1 = min(cnt3 * 2, cnt2 * 2);
      if (min(cnt2, cnt3) * 2 < max(cnt2, cnt3)) continue;
      if (lcnt1 > i + 1) continue;
      umax(lcnt1, 1);
      pair<int, int> heh = get(i - rcnt1, i - lcnt1);
      pair<int, pair<int, int> > kek = {b[j], {b[i], heh.first}};
      if (kek > aaa) {
        aaa = kek;
        first = heh.second;
        second = i;
        t = j;
      }
    }
  }
  vector<int> ans(n, -1);
  for (int i = 0; i < n; i++) {
    assert(a[i].second < n);
    if (i > t)
      ans[a[i].second] = 1;
    else if (i > second)
      ans[a[i].second] = 2;
    else if (i > first)
      ans[a[i].second] = 3;
    else
      ans[a[i].second] = -1;
  }
  for (auto& z : ans) cout << z << ' ';
  return 0;
}

```