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.InputStreamReader;
import java.util.Arrays;
import java.util.Scanner;

public class LittlePonyAndHarmonyChest {

	public static void main(String[] args) {
		Scanner in = new Scanner(new BufferedReader(new InputStreamReader(System.in)));
		int n = in.nextInt();
		int[] a = getIntArr(in, n);
		int[] b = solve(n, a);
		System.out.println(str(b));
		in.close();
	}

	private static int[] solve(int n, int[] a) {
		int[] fact = new int[60];
		int[] primes = new int[] { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59 };
		for (int i = 1; i < fact.length; i++) {
			for (int j = 0; j < primes.length; j++) {
				if (i % primes[j] == 0) {
					fact[i] |= 1 << j;
				}
			}
		}
		int globalMask = (1 << 17) - 1;
		int[][] dp = new int[n + 1][1 << 17];
		int[][] solution = new int[n + 1][1 << 17];
		int[] b = new int[n];
		for (int i = 1; i <= n; i++) {
			Arrays.fill(dp[i], Integer.MAX_VALUE);
			for (int k = 1; k < 60; k++) {
				int maskOtherPrimes = (~fact[k]) & (globalMask);
				int s = maskOtherPrimes;
				int diff = Math.abs(a[i - 1] - k);
				while (s != 0) {
					if (dp[i][fact[k] | s] > dp[i - 1][s] + diff) {
						dp[i][fact[k] | s] = dp[i - 1][s] + diff;
						solution[i][fact[k] | s] = k;
					}
					s = (s - 1) & maskOtherPrimes;
				}
			}
		}
		int min = Integer.MAX_VALUE;
		int mask = 0;
		for (int i = 0; i < dp[n].length; i++) {
			if (min > dp[n][i]) {
				min = dp[n][i];
				b[n - 1] = solution[n][i];
				mask = i;
			}
		}

		for (int i = n - 2; i >= 0; i--) {
			mask = mask & (~fact[b[i + 1]]) & globalMask;
			b[i] = solution[i + 1][mask];
		}
		return b;
	}

	static String str(int[] a) {
		String[] str = new String[a.length];
		for (int i = 0; i < a.length; i++) {
			str[i] = a[i] + "";
		}
		return String.join(" ", str);
	}

	static int[] getIntArr(Scanner in, int size) {
		int[] arr = new int[size];
		for (int i = 0; i < size; i++) {
			arr[i] = in.nextInt();
		}
		return arr;
	}

	static int[][] getIntArr(Scanner in, int row, int col) {
		int[][] arr = new int[row][];
		for (int i = 0; i < row; i++) {
			arr[i] = getIntArr(in, col);
		}
		return arr;
	}

	static char[] getCharArr(Scanner in, int size) {
		char[] arr = in.next().toCharArray();
		return arr;
	}

	static String[] getStringArr(Scanner in, int size) {
		String[] arr = new String[size];
		for (int i = 0; i < size; i++) {
			arr[i] = in.next();
		}
		return arr;
	}

}