#include <bits/stdc++.h>
using namespace std;
inline int min(const int &x, const int &y) { return x < y ? x : y; }
inline long long min(const long long &x, const long long &y) {
  return x < y ? x : y;
}
inline double min(const double &x, const double &y) { return x < y ? x : y; }
inline int max(const int &x, const int &y) { return x > y ? x : y; }
inline long long max(const long long &x, const long long &y) {
  return x > y ? x : y;
}
inline double max(const double &x, const double &y) { return x > y ? x : y; }
template <class T>
inline void _updmin(T &x, const T &y) {
  if (x > y) x = y;
}
template <class T>
inline void _updmax(T &x, const T &y) {
  if (x < y) x = y;
}
template <class T>
inline T _lowbit(const T &x) {
  return (x ^ (x - 1)) & x;
}
template <class T>
inline int _bitsize(const T &x) {
  return (x == 0) ? 0 : (1 + _bitsize(x & (x - 1)));
}
const double _pi = acos(-1.0);
const double _eps = 1e-5;
template <class T>
inline T _sqr(const T &x) {
  return x * x;
}
template <class T>
inline T _pow(T x, T y) {
  if (y == 0)
    return 1;
  else if ((y & 1) == 0) {
    T z = _pow(x, y >> 1);
    return z * z;
  } else
    return _pow(x, y ^ 1) * x;
}
template <class T>
inline T _gcd(const T &x, const T &y) {
  if (x < 0) return _gcd(-x, y);
  if (y < 0) return _gcd(x, -y);
  return (y == 0) ? x : _gcd(y, x % y);
}
template <class T>
inline T _lcm(const T &x, const T &y) {
  if (x < 0) return _lcm(-x, y);
  if (y < 0) return _lcm(x, -y);
  return x * (y / _gcd(x, y));
}
template <class T>
inline T _euc(const T &a, const T &b, T &x, T &y) {
  if (a < 0) {
    T d = _euc(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = _euc(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = _euc(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <class T>
inline vector<pair<T, int> > _fac(T n) {
  vector<pair<T, int> > ret;
  for (T i = 2; n > 1;) {
    if (n % i == 0) {
      int cnt = 0;
      for (; n % i == 0; cnt++, n /= i)
        ;
      ret.push_back(make_pair(i, cnt));
    }
    i++;
    if (i > n / i) i = n;
  }
  if (n > 1) ret.push_back(make_pair(n, 1));
  return ret;
}
template <class T>
inline int _prm(const T &x) {
  if (x <= 1) return 0;
  for (T i = 2; sqr(i) <= x; i++)
    if (x % i == 0) return 0;
  return 1;
}
template <class T>
inline T _phi(T x) {
  vector<pair<T, int> > f = _fac(x);
  T ret = x;
  for (int i = 0; i < ((int)(f.size())); i++)
    ret = ret / f[i].first * (f[i].first - 1);
  return ret;
}
template <class T>
inline T _inv(T a, T b) {
  T x, y;
  _euc(a, b, x, y);
  if (x == 0) x = 1;
  return x;
}
template <class T>
inline T _cmod(T x, T m) {
  return (x % m + m) % m;
}
template <class T>
inline T _amod(T x, T y, T m) {
  return ((x + y) % m + m) % m;
}
template <class T>
inline T _mmod(T x, T y, T m) {
  return (
      T)((((long long)x) * ((long long)y) % ((long long)m) + ((long long)m)) %
         ((long long)m));
}
template <class T>
inline T _pmod(T x, T y, T m) {
  if (y == 0)
    return 1 % m;
  else if ((y & 1) == 0) {
    T z = _pmod(x, y >> 1, m);
    return _mmod(z, z, m);
  } else
    return _mmod(_pmod(x, y ^ 1, m), x, m);
}
template <class T>
inline void _addMod(T &x, T y, T m) {
  x = ((x + y) % m + m) % m;
}
template <class T>
inline void _mulMod(T &x, T y, T m) {
  x = (T)((((long long)x) * ((long long)y) % ((long long)m) + ((long long)m)) %
          ((long long)m));
}
const int _MTRXSIZE = 40;
template <class T>
inline void _shwMTRX(int n, T A[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) cout << A[i][j] << " ";
    cout << endl;
  }
}
template <class T>
inline void _stdMTRX(int n, T A[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) A[i][j] = (i == j) ? 1 : 0;
}
template <class T>
inline void _addMTRX(int n, T C[_MTRXSIZE][_MTRXSIZE],
                     T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = A[i][j] + B[i][j];
}
template <class T>
inline void _subMTRX(int n, T C[_MTRXSIZE][_MTRXSIZE],
                     T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = A[i][j] - B[i][j];
}
template <class T>
inline void _mulMTRX(int n, T C[_MTRXSIZE][_MTRXSIZE],
                     T _A[_MTRXSIZE][_MTRXSIZE], T _B[_MTRXSIZE][_MTRXSIZE]) {
  T A[_MTRXSIZE][_MTRXSIZE], B[_MTRXSIZE][_MTRXSIZE];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) {
      A[i][j] = _A[i][j];
      B[i][j] = _B[i][j];
      C[i][j] = 0;
    }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      for (int k = 0; k < n; k++) C[i][j] += A[i][k] * B[k][j];
}
template <class T>
inline void _addModMTRX(int n, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = _cmod(A[i][j] + B[i][j], m);
}
template <class T>
inline void _subModMTRX(int n, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = _cmod(A[i][j] - B[i][j], m);
}
template <class T>
inline void _mulModMTRX(int n, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T _A[_MTRXSIZE][_MTRXSIZE],
                        T _B[_MTRXSIZE][_MTRXSIZE]) {
  T A[_MTRXSIZE][_MTRXSIZE], B[_MTRXSIZE][_MTRXSIZE];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) {
      A[i][j] = _A[i][j];
      B[i][j] = _B[i][j];
      C[i][j] = 0;
    }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      for (int k = 0; k < n; k++)
        C[i][j] = (C[i][j] + _mmod(A[i][k], B[k][j], m)) % m;
}
template <class T>
inline void _powModMTRX(int n, T y, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T X[_MTRXSIZE][_MTRXSIZE]) {
  T R[_MTRXSIZE][_MTRXSIZE];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) R[i][j] = X[i][j];
  _stdMTRX(n, C);
  if (y > 0)
    for (T i = 1;; i <<= 1) {
      if (y & i) _mulModMTRX(n, m, C, C, R);
      _mulModMTRX(n, m, R, R, R);
      if (i > (y >> 1)) break;
    }
}
template <class T>
struct _frct {
  T a, b;
  _frct(T a = 0, T b = 1);
  string toString();
};
template <class T>
_frct<T>::_frct(T a, T b) {
  T d = _gcd(a, b);
  a /= d;
  b /= d;
  if (b < 0) a = -a, b = -b;
  this->a = a;
  this->b = b;
}
template <class T>
string _frct<T>::toString() {
  ostringstream tout;
  tout << a << "/" << b;
  return tout.str();
}
template <class T>
_frct<T> operator+(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.b + q.a * p.b, p.b * q.b);
}
template <class T>
_frct<T> operator-(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.b - q.a * p.b, p.b * q.b);
}
template <class T>
_frct<T> operator*(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.a, p.b * q.b);
}
template <class T>
_frct<T> operator/(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.b, p.b * q.a);
}
const int inf = 0x3f3f3f3f;
int prm[60], pnm, sb[60];
int f[110][200000], g[110][200000], c[110][200000];
int n, a[110], ans[110], key, bit[20];
queue<int> que[110];
void init() {
  pnm = 0;
  for (int i = 2; i < 60; i++) {
    int flag = 1;
    for (int p = 0; p < pnm; p++) {
      if ((i % prm[p]) == 0) {
        flag = 0;
        break;
      }
    }
    if (flag) prm[pnm++] = i;
  }
  for (int i = 0; i <= pnm; i++) bit[i] = (1 << (i));
  for (int i = 0; i < 60; i++) {
    sb[i] = 0;
    for (int p = 0; p < pnm; p++)
      if ((i % prm[p]) == 0) sb[i] |= bit[p];
  }
}
int main() {
  init();
  while (scanf("%d", &n) != EOF) {
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
      while (!que[i].empty()) que[i].pop();
    }
    memset(f, 0x3f, sizeof(f));
    f[0][0] = 0;
    que[0].push(0);
    for (int i = 0; i < n; i++) {
      for (; !que[i].empty(); que[i].pop()) {
        int j = que[i].front();
        for (int k = 1; k < 60; k++) {
          if (j & sb[k]) continue;
          int val = f[i][j] + abs(k - a[i]);
          int sta = j | sb[k];
          if (val < f[i + 1][sta]) {
            if (i + 1 < n && f[i + 1][sta] == inf) que[i + 1].push(sta);
            f[i + 1][sta] = val;
            g[i + 1][sta] = j;
            c[i + 1][sta] = k;
          }
        }
      }
    }
    key = 0;
    for (int i = 1; i < 200000; i++)
      if (f[n][key] > f[n][i]) key = i;
    for (int i = n; i; i--) {
      ans[i - 1] = c[i][key];
      key = g[i][key];
    }
    for (int i = 0; i < n; i++) {
      if (i) printf(" ");
      printf("%d", ans[i]);
    }
    printf("\n");
  }
  return 0;
}

### Prompt

Construct a cpp code solution to the problem outlined:

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

<image>

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:

<image>

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 

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
inline int min(const int &x, const int &y) { return x < y ? x : y; }
inline long long min(const long long &x, const long long &y) {
  return x < y ? x : y;
}
inline double min(const double &x, const double &y) { return x < y ? x : y; }
inline int max(const int &x, const int &y) { return x > y ? x : y; }
inline long long max(const long long &x, const long long &y) {
  return x > y ? x : y;
}
inline double max(const double &x, const double &y) { return x > y ? x : y; }
template <class T>
inline void _updmin(T &x, const T &y) {
  if (x > y) x = y;
}
template <class T>
inline void _updmax(T &x, const T &y) {
  if (x < y) x = y;
}
template <class T>
inline T _lowbit(const T &x) {
  return (x ^ (x - 1)) & x;
}
template <class T>
inline int _bitsize(const T &x) {
  return (x == 0) ? 0 : (1 + _bitsize(x & (x - 1)));
}
const double _pi = acos(-1.0);
const double _eps = 1e-5;
template <class T>
inline T _sqr(const T &x) {
  return x * x;
}
template <class T>
inline T _pow(T x, T y) {
  if (y == 0)
    return 1;
  else if ((y & 1) == 0) {
    T z = _pow(x, y >> 1);
    return z * z;
  } else
    return _pow(x, y ^ 1) * x;
}
template <class T>
inline T _gcd(const T &x, const T &y) {
  if (x < 0) return _gcd(-x, y);
  if (y < 0) return _gcd(x, -y);
  return (y == 0) ? x : _gcd(y, x % y);
}
template <class T>
inline T _lcm(const T &x, const T &y) {
  if (x < 0) return _lcm(-x, y);
  if (y < 0) return _lcm(x, -y);
  return x * (y / _gcd(x, y));
}
template <class T>
inline T _euc(const T &a, const T &b, T &x, T &y) {
  if (a < 0) {
    T d = _euc(-a, b, x, y);
    x = -x;
    return d;
  }
  if (b < 0) {
    T d = _euc(a, -b, x, y);
    y = -y;
    return d;
  }
  if (b == 0) {
    x = 1;
    y = 0;
    return a;
  } else {
    T d = _euc(b, a % b, x, y);
    T t = x;
    x = y;
    y = t - (a / b) * y;
    return d;
  }
}
template <class T>
inline vector<pair<T, int> > _fac(T n) {
  vector<pair<T, int> > ret;
  for (T i = 2; n > 1;) {
    if (n % i == 0) {
      int cnt = 0;
      for (; n % i == 0; cnt++, n /= i)
        ;
      ret.push_back(make_pair(i, cnt));
    }
    i++;
    if (i > n / i) i = n;
  }
  if (n > 1) ret.push_back(make_pair(n, 1));
  return ret;
}
template <class T>
inline int _prm(const T &x) {
  if (x <= 1) return 0;
  for (T i = 2; sqr(i) <= x; i++)
    if (x % i == 0) return 0;
  return 1;
}
template <class T>
inline T _phi(T x) {
  vector<pair<T, int> > f = _fac(x);
  T ret = x;
  for (int i = 0; i < ((int)(f.size())); i++)
    ret = ret / f[i].first * (f[i].first - 1);
  return ret;
}
template <class T>
inline T _inv(T a, T b) {
  T x, y;
  _euc(a, b, x, y);
  if (x == 0) x = 1;
  return x;
}
template <class T>
inline T _cmod(T x, T m) {
  return (x % m + m) % m;
}
template <class T>
inline T _amod(T x, T y, T m) {
  return ((x + y) % m + m) % m;
}
template <class T>
inline T _mmod(T x, T y, T m) {
  return (
      T)((((long long)x) * ((long long)y) % ((long long)m) + ((long long)m)) %
         ((long long)m));
}
template <class T>
inline T _pmod(T x, T y, T m) {
  if (y == 0)
    return 1 % m;
  else if ((y & 1) == 0) {
    T z = _pmod(x, y >> 1, m);
    return _mmod(z, z, m);
  } else
    return _mmod(_pmod(x, y ^ 1, m), x, m);
}
template <class T>
inline void _addMod(T &x, T y, T m) {
  x = ((x + y) % m + m) % m;
}
template <class T>
inline void _mulMod(T &x, T y, T m) {
  x = (T)((((long long)x) * ((long long)y) % ((long long)m) + ((long long)m)) %
          ((long long)m));
}
const int _MTRXSIZE = 40;
template <class T>
inline void _shwMTRX(int n, T A[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < n; j++) cout << A[i][j] << " ";
    cout << endl;
  }
}
template <class T>
inline void _stdMTRX(int n, T A[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) A[i][j] = (i == j) ? 1 : 0;
}
template <class T>
inline void _addMTRX(int n, T C[_MTRXSIZE][_MTRXSIZE],
                     T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = A[i][j] + B[i][j];
}
template <class T>
inline void _subMTRX(int n, T C[_MTRXSIZE][_MTRXSIZE],
                     T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = A[i][j] - B[i][j];
}
template <class T>
inline void _mulMTRX(int n, T C[_MTRXSIZE][_MTRXSIZE],
                     T _A[_MTRXSIZE][_MTRXSIZE], T _B[_MTRXSIZE][_MTRXSIZE]) {
  T A[_MTRXSIZE][_MTRXSIZE], B[_MTRXSIZE][_MTRXSIZE];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) {
      A[i][j] = _A[i][j];
      B[i][j] = _B[i][j];
      C[i][j] = 0;
    }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      for (int k = 0; k < n; k++) C[i][j] += A[i][k] * B[k][j];
}
template <class T>
inline void _addModMTRX(int n, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = _cmod(A[i][j] + B[i][j], m);
}
template <class T>
inline void _subModMTRX(int n, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T A[_MTRXSIZE][_MTRXSIZE], T B[_MTRXSIZE][_MTRXSIZE]) {
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) C[i][j] = _cmod(A[i][j] - B[i][j], m);
}
template <class T>
inline void _mulModMTRX(int n, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T _A[_MTRXSIZE][_MTRXSIZE],
                        T _B[_MTRXSIZE][_MTRXSIZE]) {
  T A[_MTRXSIZE][_MTRXSIZE], B[_MTRXSIZE][_MTRXSIZE];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) {
      A[i][j] = _A[i][j];
      B[i][j] = _B[i][j];
      C[i][j] = 0;
    }
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++)
      for (int k = 0; k < n; k++)
        C[i][j] = (C[i][j] + _mmod(A[i][k], B[k][j], m)) % m;
}
template <class T>
inline void _powModMTRX(int n, T y, T m, T C[_MTRXSIZE][_MTRXSIZE],
                        T X[_MTRXSIZE][_MTRXSIZE]) {
  T R[_MTRXSIZE][_MTRXSIZE];
  for (int i = 0; i < n; i++)
    for (int j = 0; j < n; j++) R[i][j] = X[i][j];
  _stdMTRX(n, C);
  if (y > 0)
    for (T i = 1;; i <<= 1) {
      if (y & i) _mulModMTRX(n, m, C, C, R);
      _mulModMTRX(n, m, R, R, R);
      if (i > (y >> 1)) break;
    }
}
template <class T>
struct _frct {
  T a, b;
  _frct(T a = 0, T b = 1);
  string toString();
};
template <class T>
_frct<T>::_frct(T a, T b) {
  T d = _gcd(a, b);
  a /= d;
  b /= d;
  if (b < 0) a = -a, b = -b;
  this->a = a;
  this->b = b;
}
template <class T>
string _frct<T>::toString() {
  ostringstream tout;
  tout << a << "/" << b;
  return tout.str();
}
template <class T>
_frct<T> operator+(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.b + q.a * p.b, p.b * q.b);
}
template <class T>
_frct<T> operator-(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.b - q.a * p.b, p.b * q.b);
}
template <class T>
_frct<T> operator*(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.a, p.b * q.b);
}
template <class T>
_frct<T> operator/(_frct<T> p, _frct<T> q) {
  return _frct<T>(p.a * q.b, p.b * q.a);
}
const int inf = 0x3f3f3f3f;
int prm[60], pnm, sb[60];
int f[110][200000], g[110][200000], c[110][200000];
int n, a[110], ans[110], key, bit[20];
queue<int> que[110];
void init() {
  pnm = 0;
  for (int i = 2; i < 60; i++) {
    int flag = 1;
    for (int p = 0; p < pnm; p++) {
      if ((i % prm[p]) == 0) {
        flag = 0;
        break;
      }
    }
    if (flag) prm[pnm++] = i;
  }
  for (int i = 0; i <= pnm; i++) bit[i] = (1 << (i));
  for (int i = 0; i < 60; i++) {
    sb[i] = 0;
    for (int p = 0; p < pnm; p++)
      if ((i % prm[p]) == 0) sb[i] |= bit[p];
  }
}
int main() {
  init();
  while (scanf("%d", &n) != EOF) {
    for (int i = 0; i < n; i++) {
      scanf("%d", &a[i]);
      while (!que[i].empty()) que[i].pop();
    }
    memset(f, 0x3f, sizeof(f));
    f[0][0] = 0;
    que[0].push(0);
    for (int i = 0; i < n; i++) {
      for (; !que[i].empty(); que[i].pop()) {
        int j = que[i].front();
        for (int k = 1; k < 60; k++) {
          if (j & sb[k]) continue;
          int val = f[i][j] + abs(k - a[i]);
          int sta = j | sb[k];
          if (val < f[i + 1][sta]) {
            if (i + 1 < n && f[i + 1][sta] == inf) que[i + 1].push(sta);
            f[i + 1][sta] = val;
            g[i + 1][sta] = j;
            c[i + 1][sta] = k;
          }
        }
      }
    }
    key = 0;
    for (int i = 1; i < 200000; i++)
      if (f[n][key] > f[n][i]) key = i;
    for (int i = n; i; i--) {
      ans[i - 1] = c[i][key];
      key = g[i][key];
    }
    for (int i = 0; i < n; i++) {
      if (i) printf(" ");
      printf("%d", ans[i]);
    }
    printf("\n");
  }
  return 0;
}

```