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 JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class R259qBLittleHarmonyAndChest {

	public static void main(String args[]) {
		InputReader in = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
		
		long start = System.currentTimeMillis();
		int primeSet[] = new int[61];
		int primeCount = 0;
		
		for(int i=2;i<=58;i++){
			if(primeSet[i] == 0){
				for(int j=i;j<=58;j+=i)
					primeSet[j] = set(primeCount,primeSet[j]);
				primeCount++;
			}
		}
		
		int n = in.nextInt();
		
		int a[] = new int[n];
		for(int i=0;i<n;i++)
			a[i] = in.nextInt();
		
		int dp[][] = new int[n + 1][1<<primeCount];
		int val[][] = new int[n + 1][1<<primeCount];
		
		final int oo = Integer.MAX_VALUE >> 1;
		
		for(int i=n-1;i>=0;i--){
			for(int mask=0;mask<(1<<primeCount);mask++){
				dp[i][mask] = oo;
				for(int j=1;j<=58;j++){
					if((mask & primeSet[j]) == 0){
						int wow = Math.abs(a[i] - j) + dp[i+1][mask|primeSet[j]];
						if(wow < dp[i][mask]){
							dp[i][mask] = wow;
							val[i][mask] = j;
						}
					}
				}
			}
		}
		
		int mask = 0;
		for(int i=0;i<n;i++){
			w.print(val[i][mask] + " ");
			mask = mask | primeSet[val[i][mask]];
		}
		
		w.println();
		w.close();
		
		System.out.println(System.currentTimeMillis() - start);
	}
	
	static boolean get(int bit,int mask){
		return (mask & (1<<bit)) != 0;
	}
	
	static int set(int bit,int mask){
		return mask | (1 << bit);
	}
	
	static class InputReader {

		private InputStream stream;
		private byte[] buf = new byte[8192];
		private int curChar;
		private int snumChars;
		private SpaceCharFilter filter;

		public InputReader(InputStream stream) {
			this.stream = stream;
		}

		public int snext() {
			if (snumChars == -1)
				throw new InputMismatchException();
			if (curChar >= snumChars) {
				curChar = 0;
				try {
					snumChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (snumChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		public int nextInt() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			int res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public long nextLong() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = snext();
			}

			long res = 0;

			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = snext();
			} while (!isSpaceChar(c));

			return res * sgn;
		}
		
		public String readString() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
}