Problem: 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 

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <class T>
inline T MIN_3(T a, T b, T c) {
  return min(min(a, b), c);
}
template <class T>
inline T MAX_3(T a, T b, T c) {
  return max(max(a, b), c);
}
template <class T>
inline T BIGMOD(T n, T m, T mod) {
  long long int ans = 1;
  long long int k = n;
  while (m) {
    if (m & 1) {
      ans *= k;
      if (ans > mod) ans %= mod;
    }
    k *= k;
    if (k > mod) k %= mod;
    m >>= 1;
  }
  return ans;
}
template <class T>
string toString(T n) {
  ostringstream ost;
  ost << n;
  ost.flush();
  return ost.str();
}
template <class T>
string toBinary(T n) {
  string ret = "";
  while (n) {
    if (n % 2 == 1)
      ret += '1';
    else
      ret += '0';
    n >>= 1;
  }
  reverse(ret.begin(), ret.end());
  return ret;
}
void combination(int n, vector<vector<int> > &ret) {
  ret.resize(n + 1, vector<int>(n + 1, 0));
  for (int i = 1; i <= n; i++) {
    ret[i][0] = ret[i][i] = 1;
    for (int j = 1; j < i; j++) {
      ret[i][j] = ret[i - 1][j] + ret[i - 1][j - 1];
    }
  }
}
int toInt(string s) {
  int r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
long long int toLInt(string s) {
  long long int r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
double toDouble(string s) {
  double r = 0;
  istringstream sin(s);
  sin >> r;
  return r;
}
vector<string> parse(string temp) {
  vector<string> ans;
  ans.clear();
  string s;
  istringstream iss(temp);
  while (iss >> s) ans.push_back(s);
  return ans;
}
template <class T>
inline T gcd(T a, T b) {
  if (a < 0) return gcd(-a, b);
  if (b < 0) return gcd(a, -b);
  return (b == 0) ? a : gcd(b, a % b);
}
template <class T>
inline T lcm(T a, T b) {
  if (a < 0) return lcm(-a, b);
  if (b < 0) return lcm(a, -b);
  return a * (b / gcd(a, b));
}
template <class T>
inline T power(T b, T p) {
  if (p < 0) return -1;
  if (b <= 0) return -2;
  if (!p) return 1;
  return b * power(b, p - 1);
}
template <class T>
inline int asd(T &ret) {
  char r;
  bool start = false, neg = false;
  ret = 0;
  bool isaNumber = false;
  while (true) {
    r = getchar();
    if (r == EOF) {
      return 0;
    }
    if ((r - '0' < 0 || r - '0' > 9) && r != '-' && !start) {
      continue;
    }
    if ((r - '0' < 0 || r - '0' > 9) && r != '-' && start) {
      break;
    }
    if (start) ret *= 10;
    start = true;
    if (r == '-')
      neg = true;
    else
      ret += r - '0';
  }
  if (neg) ret *= -1;
  return 1;
}
template <class T>
inline void asdasd(T x, char y) {
  if (x < 0) {
    putchar('-');
    x = -x;
  }
  char buf[21], *p = buf;
  do {
    *p++ = '0' + x % 10;
    x /= 10;
  } while (x);
  do {
    putchar(*--p);
  } while (p > buf);
  if (y == 0)
    putchar('\n');
  else if (y == 1)
    putchar(' ');
}
vector<int> pr;
int inp[101];
int dp[101][1 << 16];
int go[101][1 << 16];
int n;
int bp[61];
void make(int &ret, int n) {
  for (int i = 0; i <= pr.size() - 1; i++) {
    if (n % pr[i] == 0) ret |= (1 << i);
  }
}
int inf = 100000000, sat = (1 << 16) - 1;
int rec(int pos, int mask) {
  if (pos == n) return 0;
  int &ret = dp[pos][mask];
  if (ret != -1) return ret;
  ret = inf;
  int now;
  for (int i = 1; i <= 58; i++) {
    if ((bp[i] & mask) == 0) {
      now = abs(inp[pos] - i) + rec(pos + 1, mask | bp[i]);
      if (ret > now) {
        ret = now;
        go[pos][mask] = i;
      }
    }
  }
  return ret;
}
vector<int> ans;
void path(int pos, int mask) {
  if (pos == n) return;
  ans.push_back(go[pos][mask]);
  path(pos + 1, mask | bp[go[pos][mask]]);
}
int main() {
  for (int i = 2; i <= 60; i++) {
    bool ok = true;
    for (int j = 2; j < i; j++) {
      if (i % j == 0) {
        ok = false;
        break;
      }
    }
    if (ok) pr.push_back(i);
  }
  for (int i = 2; i <= 60; i++) {
    make(bp[i], i);
  }
  asd(n);
  for (int i = 0; i <= n - 1; i++) {
    asd(inp[i]);
  }
  memset(dp, -1, sizeof(dp));
  rec(0, 0);
  path(0, 0);
  for (int i = 0; i <= ans.size() - 1; i++) asdasd(ans[i], i != ans.size() - 1);
  return 0;
}