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 JAVA):

Solution:
import sun.security.krb5.internal.crypto.Des;

import java.io.*;
import java.util.*;

public class Template implements Runnable {

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");

    void init() throws FileNotFoundException {
        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            try {
                tok = new StringTokenizer(in.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return tok.nextToken();
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    int[] readIntArray(int size) throws IOException {
        int[] res = new int[size];
        for (int i = 0; i < size; i++) {
            res[i] = readInt();
        }
        return res;
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    <T> List<T>[] createGraphList(int size) {
        List<T>[] list = new List[size];
        for (int i = 0; i < size; i++) {
            list[i] = new ArrayList<>();
        }
        return list;
    }

    public static void main(String[] args) {
        new Template().run();
        // new Thread(null, new Template(), "", 1l * 200 * 1024 * 1024).start();
    }

    long timeBegin, timeEnd;

    void time() {
        timeEnd = System.currentTimeMillis();
        System.err.println("Time = " + (timeEnd - timeBegin));
    }

    long memoryTotal, memoryFree;

    void memory() {
        memoryFree = Runtime.getRuntime().freeMemory();
        System.err.println("Memory = " + ((memoryTotal - memoryFree) >> 10)
                + " KB");
    }

    public void run() {
        try {
            timeBegin = System.currentTimeMillis();
            memoryTotal = Runtime.getRuntime().freeMemory();
            init();
            solve();
            out.close();
            if (System.getProperty("ONLINE_JUDGE") == null) {
                time();
                memory();
            }
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(-1);
        }
    }

    boolean isPrime(int x) {
        for (int i = 2; i < x; i++) {
            if (x % i == 0) return false;
        }
        return true;
    }

    void solve() throws IOException {
        int n = readInt();
        int[] a = readIntArray(n);
        int[] primes = new int[60];
        for (int i = 0; i < 60; i++) {
            int x = i;
            int index = 0;
            for (int j = 2; j <= x; j++) {
                if (isPrime(j)) {
                    if (x % j == 0) {
                        primes[i] |= 1 << index;
                    }
                    index++;
                }
            }
            //System.err.println(index);
        }
        int max = 1 << 17;
        int[][] dp = new int[n + 1][max];
        int[][] parentValue = new int[n + 1][max];
        for (int[] x : dp) {
            Arrays.fill(x, Integer.MAX_VALUE);
        }
        dp[0][0] = 0;
        int[][] allowedNexts = new int[max][];
        int allSize = 0;
        for (int mask = 0; mask < max; mask++) {
            List<Integer> list = new ArrayList<>();
            for (int num = 1; num < 60; num++) {
                if ((mask & primes[num]) == 0) {
                    list.add(num);
                }
            }
            allowedNexts[mask] = new int[list.size()];
            for (int i = 0; i < list.size(); i++) {
                allowedNexts[mask][i] = list.get(i);
            }
            allSize += list.size();
        }
        for (int i = 1; i <= n; i++) {
            for (int prevMask = 0; prevMask < max; prevMask++) {
                if (dp[i - 1][prevMask] == Integer.MAX_VALUE) continue;
                for (int num : allowedNexts[prevMask]) {
                    int nextVal = dp[i - 1][prevMask] + Math.abs(a[i - 1] - num);
                    int nextMask = prevMask | primes[num];
                    if (nextVal < dp[i][nextMask]) {
                        dp[i][nextMask] = nextVal;
                        parentValue[i][nextMask] = num;
                    }
                }
            }
        }

        int[] b = new int[n];
        int minMask = 0;
        for (int mask = 0; mask < max; mask++) {
            if (dp[n][mask] < dp[n][minMask]) {
                minMask = mask;
            }
        }
        for (int i = n; i > 0; i--) {
            b[i - 1] = parentValue[i][minMask];
            minMask ^= primes[b[i - 1]];
        }
        for (int x : b) out.print(x + " ");

    }


}