Problem: Princess Twilight went to Celestia and Luna's old castle to research the chest from the Elements of Harmony.

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A sequence of positive integers bi is harmony if and only if for every two elements of the sequence their greatest common divisor equals 1. According to an ancient book, the key of the chest is a harmony sequence bi which minimizes the following expression:

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You are given sequence ai, help Princess Twilight to find the key.

Input

The first line contains an integer n (1 ≤ n ≤ 100) — the number of elements of the sequences a and b. The next line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 30).

Output

Output the key — sequence bi that minimizes the sum described above. If there are multiple optimal sequences, you can output any of them.

Examples

Input

5
1 1 1 1 1


Output

1 1 1 1 1 

Input

5
1 6 4 2 8


Output

1 5 3 1 8 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
const long long mod = 1000000007;
long long powmod(long long a, long long b) {
  long long res = 1;
  a %= mod;
  assert(b >= 0);
  for (; b; b >>= 1) {
    if (b & 1) res = res * a % mod;
    a = a * a % mod;
  }
  return res % mod;
}
long long gcd(long long a, long long b) { return b ? gcd(b, a % b) : a; }
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
const std::vector<std::pair<int, int>> moves{{0, -1}, {-1, 0}, {0, 1}, {1, 0}};
inline int bitCount(long long x) { return __builtin_popcountll(x); }
inline long long highestOneBit(long long x) {
  return 1LL << (63 - __builtin_clzll(x | 1LL));
}
inline int binaryDigits(long long x) { return 64 - __builtin_clzll(x | 1LL); }
template <typename A>
string to_string(A* ptr) {
  stringstream ss;
  ss << "0x" << std::setw(16) << std::setfill('0') << std::hex
     << (uint64_t)(uintptr_t)ptr;
  return ss.str();
}
template <typename A, typename B>
string to_string(pair<A, B> p);
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p);
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p);
string to_string(const string& s) { return '"' + s + '"'; }
string to_string(const char* s) { return to_string((string)s); }
string to_string(bool b) { return (b ? "true" : "false"); }
string to_string(vector<bool> v) {
  bool first = true;
  string res = "{";
  for (int i = 0; i < static_cast<int>(v.size()); i++) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(v[i]);
  }
  res += "}";
  return res;
}
template <size_t N>
string to_string(bitset<N> v) {
  string res = "";
  for (size_t i = 0; i < N; i++) {
    res += static_cast<char>('0' + v[i]);
  }
  return res;
}
template <typename A>
string to_string(A v) {
  bool first = true;
  string res = "{";
  for (const auto& x : v) {
    if (!first) {
      res += ", ";
    }
    first = false;
    res += to_string(x);
  }
  res += "}";
  return res;
}
template <typename A, typename B>
string to_string(pair<A, B> p) {
  return "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
}
template <typename A, typename B, typename C>
string to_string(tuple<A, B, C> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ")";
}
template <typename A, typename B, typename C, typename D>
string to_string(tuple<A, B, C, D> p) {
  return "(" + to_string(get<0>(p)) + ", " + to_string(get<1>(p)) + ", " +
         to_string(get<2>(p)) + ", " + to_string(get<3>(p)) + ")";
}
void debug_out() { cerr << '\n'; }
template <typename Head, typename... Tail>
void debug_out(Head H, Tail... T) {
  cerr << " " << to_string(H);
  debug_out(T...);
}
vector<int> prime = {2,  3,  5,  7,  11, 13, 17, 19, 23,
                     29, 31, 37, 41, 43, 47, 53, 59};
vector<int> f(60);
void precalc() {
  for (int i = 1; i < 60; i++) {
    int msk = 0;
    for (int j = 0; j < 17; j++) {
      if (i % prime[j] == 0) msk |= (1 << j);
    }
    f[i] = msk;
  }
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  precalc();
  int n;
  cin >> n;
  vector<int> a(n);
  for (int i = 0; i < n; i++) cin >> a[i];
  vector<vector<int>> dp(1 << 16, vector<int>(n + 1, 1e9));
  for (int i = 0; i < 1 << 16; i++) dp[i][0] = 0;
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < 1 << 16; j++) {
      for (int k = 1; k < 59; k++) {
        if (f[k] & j)
          continue;
        else {
          dp[f[k] | j][i + 1] =
              min(dp[f[k] | j][i + 1], dp[j][i] + abs(k - a[i]));
        }
      }
    }
  }
  int msk = 0;
  for (int i = 0; i < 1 << 16; i++) {
    if (dp[msk][n] > dp[i][n]) {
      msk = i;
    }
  }
  vector<int> ans;
  for (int i = n - 1; i >= 0; i--) {
    for (int k = 1; k < 59; k++) {
      if ((msk & f[k]) != f[k]) continue;
      if (dp[msk][i + 1] == dp[msk ^ f[k]][i] + abs(k - a[i])) {
        ans.push_back(k);
        msk ^= f[k];
        break;
      }
    }
  }
  assert(((int)(ans).size()) == n);
  for (int i = n - 1; i >= 0; i--) cout << ans[i] << " \n"[i == 0];
}