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 java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.*;

public class HarmonyChest3 {
    static boolean test = false;

    static class Item {
        public int a;
        public int pos;
        public int b;

        public Item(int a, int pos) {
            this.a = a;
            this.pos = pos;
        }
    }

    static int n; // 100
    static Item[] a; // 1..30
    static Comparator<Item> posComparator = new Comparator<HarmonyChest3.Item>() {
        @Override
        public int compare(Item arg0, Item arg1) {
            return Integer.compare(arg0.pos, arg1.pos);
        }
    };
    static Comparator<Item> valueComparator = new Comparator<HarmonyChest3.Item>() {
        @Override
        public int compare(Item arg0, Item arg1) {
            return Integer.compare(arg0.a, arg1.a);
        }
    };
    static int[] primes = new int[] { 1, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29,
            31, 37, 41, 43, 47, 53, 59 };
    static boolean[][] map = new boolean[61][61];

    public static void main(String[] args) throws IOException {

        initReader();
        logTime("");
        buildMap();

        while (true) {
            readInput();

            logTime("Read:");
            solve();
            logTime("Solved:");

            Arrays.sort(a, posComparator);
            StringBuilder sOut = new StringBuilder();
            for (int i = 0; i < n; i++) {
                sOut.append(a[i].b + " ");
            }
            System.out.println(sOut);

            if (!test)
                break;
        }

    }

    public static void solve() {
        Arrays.sort(a, valueComparator);

        int primeLen = primes.length;
        int start = Math.max(n - primeLen + 1, 0);
        for (int i = 0; i < start; i++) {
            a[i].b = 1;
        }

        int len = n - start;
        bOptions = new short[len][39];
        indexes = new short[len];
        result = new int[len];
        short j = 0;
        for (short i = 1; i <= 53; i++) {
            if (i != 52 && i != 51 && i != 50 && i != 48 && i != 46 && i != 45
                    && i != 44 && i != 42 && i != 40 && i != 39 && i != 38
                    && i != 35 && i != 36 && i != 34 && i != 33) {
                bOptions[0][j++] = i;
            }
        }
        Arrays.fill(indexes, (short) 60);
        indexes[0] = -1;

        int[] minB = null;
        int minSum = Integer.MAX_VALUE;
        while (getNext()) {
            int sum = 0;
            for (int i = 0; i < len; i++) {
                sum += Math.abs(result[i] - a[start + i].a);
            }
            if (sum < minSum) {
                minSum = sum;
                minB = result;
                result = new int[len];
            }
        }

        for (int i = start; i < n; i++) {
            a[i].b = minB[i - start];
        }
    }

    static short[][] bOptions;
    static short[] indexes;
    static int[] result;

    public static boolean getNext() {
        int len = bOptions.length;

        int i = len - 1;
        while (i >= 0) {
            indexes[i]++;
            if (indexes[i] >= 39 || bOptions[i][indexes[i]] == 0) {
                i--;
                continue;
            }

            if (i < len - 1) {
                int current = bOptions[i][indexes[i]];
                int k = 0;
                int j = indexes[i];
                while (bOptions[i][j] != 0) {
                    if (!map[current][bOptions[i][j]]) {
                        bOptions[i + 1][k] = bOptions[i][j];
                        k++;
                    }
                    j++;
                }
                if (k < 61)
                    bOptions[i + 1][k] = 0;
                indexes[i + 1] = -1;
                i++;
                continue;
            }

            else {
                for (int j = 0; j < len; j++) {
                    result[j] = bOptions[j][indexes[j]];
                }
                return true;
            }
        }
        return false;
    }

    public static void buildMap() {
        for (int i = 1; i < primes.length; i++) {
            int p = primes[i];
            int r, c;
            for (r = p; r <= 60; r += p) {
                for (c = p; c <= 60; c += p) {
                    map[r][c] = true;
                }
            }
        }
    }

    public static void readInput() throws IOException {
        n = nextInt();
        a = new Item[n];
        for (int i = 0; i < n; i++) {
            a[i] = new Item(nextInt(), i);
        }
    }

    /*
     * Exclusives 2 4 8 16 32 | 3 9 27 | 4 8 16 36 | 5 25 | 6 8 9 12 16 18 24 27
     * 32 | 8 16 32 | 9 27 | 10 16 20 32 | 12 16 18 24 27 32 | 14 16 28 32 | 16
     * 32 | 18 24 27 32 | 20 32 | 22 32 | 24 27 32 | 26 32 | 28 32 | 30 32 |
     */

    /*****************************************************************
     ******************** BASIC READER *******************************
     *****************************************************************/

    static BufferedReader reader;
    static StringTokenizer tokenizer;

    public static void initReader() {
        reader = new BufferedReader(new InputStreamReader(System.in));
        tokenizer = new StringTokenizer("");
    }

    static String next() throws IOException {
        while (!tokenizer.hasMoreTokens()) {
            tokenizer = new StringTokenizer(reader.readLine());
        }
        return tokenizer.nextToken();
    }

    static String nextLine() throws IOException {
        return reader.readLine();
    }

    static int nextInt() throws IOException {
        return Integer.parseInt(next());
    }

    static long nextLong() throws IOException {
        return Long.parseLong(next());
    }

    static Double nextDouble() throws IOException {
        return Double.parseDouble(next());
    }

    /*****************************************************************
     ******************** TIME UTILITIES *******************************
     *****************************************************************/

    static long startTime = 0;
    static long preLogTime = 0;

    static void logTime(String lable) {
        if (!test)
            return;
        long current = System.currentTimeMillis();
        if (startTime != 0) {
            println(lable, " - From start:", (current - startTime),
                    "- From previous:", (current - preLogTime));
        } else {
            startTime = current;
        }
        preLogTime = current;
    }

    /*****************************************************************
     ******************** READ UTILITIES *******************************
     *****************************************************************/

    public static int[] readArray(int n) throws IOException {
        int[] result = new int[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextInt();
        }
        return result;
    }

    public static long[] readArrayLong(int n) throws IOException {
        long[] result = new long[n];
        for (int i = 0; i < n; i++) {
            result[i] = nextLong();
        }
        return result;
    }

    public static int[][] readMatrix(int row, int column) throws IOException {
        int[][] result = new int[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextInt();
            }
        }
        return result;
    }

    public static long[][] readMatrixLong(int row, int column)
            throws IOException {
        long[][] result = new long[row][column];
        for (int i = 0; i < row; i++) {
            for (int j = 0; j < column; j++) {
                result[i][j] = nextLong();
            }
        }
        return result;
    }

    /*****************************************************************
     ******************** PRINT UTILITIES *******************************
     *****************************************************************/

    public static void printTest(Object... obj) {
        if (!test)
            return;
        System.out.print(join(obj, " "));
    }

    public static void printTestLn(Object... obj) {
        if (!test)
            return;
        System.out.println(join(obj, " "));
    }

    public static void print(Object... obj) {
        System.out.print(join(obj, " "));
    }

    public static void println(Object... obj) {
        System.out.println(join(obj, " "));
    }

    public static String join(Object[] objs) {
        return join(objs, " ");
    }

    public static String join(int[] objs) {
        return join(objs, " ");
    }

    public static String join(long[] objs) {
        return join(objs, " ");
    }

    public static String join(Object[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(int[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static String join(long[] objs, String glue) {
        if (objs.length == 0) {
            return "";
        }
        StringBuilder sb = new StringBuilder();
        int i;
        for (i = 0; i < objs.length - 1; i++) {
            sb.append(objs[i] + glue);
        }
        return sb.toString() + objs[i];
    }

    public static void printMatrix(int[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    public static void printMatrix(long[][] matrix) {
        for (int i = 0; i < matrix.length; i++) {
            println(join(matrix[i]));
        }
    }

    /*****************************************************************
     *************** ARRAY AND STRING UTILITIES **********************
     *****************************************************************/

    public static int[] initArray(int value, int length) {
        int[] result = new int[length];
        Arrays.fill(result, value);
        return result;
    }

    public static long[] initArray(long value, int length) {
        long[] result = new long[length];
        Arrays.fill(result, value);
        return result;
    }

    public static String initString(char c, int length) {
        char[] chars = new char[length];
        Arrays.fill(chars, c);
        return new String(chars);
    }
}