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.BufferedOutputStream;
import java.io.Closeable;
import java.io.DataInputStream;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	static class TaskAdapter implements Runnable {
		@Override
		public void run() {
			long startTime = System.currentTimeMillis();
			InputStream inputStream = System.in;
			OutputStream outputStream = System.out;
			FastReader in = new FastReader(inputStream);
			Output out = new Output(outputStream);
			BLittlePonyAndHarmonyChest solver = new BLittlePonyAndHarmonyChest();
			solver.solve(1, in, out);
			out.close();
			System.err.println(System.currentTimeMillis()-startTime+"ms");
		}
	}

	public static void main(String[] args) throws Exception {
		Thread thread = new Thread(null, new TaskAdapter(), "", 1<<28);
		thread.start();
		thread.join();
	}

	static class BLittlePonyAndHarmonyChest {
		private final int iinf = 1_000_000_000;

		public BLittlePonyAndHarmonyChest() {
		}

		public void solve(int kase, InputReader in, Output pw) {
			int n = in.nextInt(), m = 17;
			int[] arr = in.nextInt(n);
			int[] mask = new int[61];
			{
				ArrayList<Integer> primes = Utilities.sieve(60);
				for(int i = 1; i<=60; i++) {
					for(int j = 0; j<m; j++) {
						if(i%primes.get(j)==0) {
							mask[i] |= 1<<j;
						}
					}
				}
			}
			int[][] dp = new int[n+1][1<<m], next = new int[n][1<<m];
			for(int i = n-1; i>=0; i--) {
				for(int j = 0; j<1<<m; j++) {
					dp[i][j] = iinf;
					for(int k = 1; k<=60; k++) {
						if((j&mask[k])==0) {
							int val = Math.abs(k-arr[i])+dp[i+1][j|mask[k]];
							if(val<dp[i][j]) {
								dp[i][j] = val;
								next[i][j] = k;
							}
						}
					}
				}
			}
			int j = 0;
			for(int i = 0; i<n; i++) {
				pw.print(next[i][j]+" ");
				j |= mask[next[i][j]];
			}
			pw.println();
		}

	}

	static class Utilities {
		public static ArrayList<Integer> sieve(int n) {
			ArrayList<Integer> ans = new ArrayList<>();
			boolean[] prime = new boolean[n+1];
			Arrays.fill(prime, true);
			for(int i = 2; i<=n; i++) {
				if(prime[i]) {
					ans.add(i);
				}
				if((long) i*i>n) {
					continue;
				}
				for(int j = i*i; j<=n; j += i) {
					prime[j] = false;
				}
			}
			return ans;
		}

	}

	static class FastReader implements InputReader {
		final private int BUFFER_SIZE = 1<<16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer;
		private int bytesRead;

		public FastReader(InputStream is) {
			din = new DataInputStream(is);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public int nextInt() {
			int ret = 0;
			byte c = skipToDigit();
			boolean neg = (c=='-');
			if(neg) {
				c = read();
			}
			do {
				ret = ret*10+c-'0';
			} while((c = read())>='0'&&c<='9');
			if(neg) {
				return -ret;
			}
			return ret;
		}

		private boolean isDigit(byte b) {
			return b>='0'&&b<='9';
		}

		private byte skipToDigit() {
			byte ret;
			while(!isDigit(ret = read())&&ret!='-') ;
			return ret;
		}

		private void fillBuffer() {
			try {
				bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			}catch(IOException e) {
				e.printStackTrace();
				throw new InputMismatchException();
			}
			if(bytesRead==-1) {
				buffer[0] = -1;
			}
		}

		private byte read() {
			if(bytesRead==-1) {
				throw new InputMismatchException();
			}else if(bufferPointer==bytesRead) {
				fillBuffer();
			}
			return buffer[bufferPointer++];
		}

	}

	static interface InputReader {
		int nextInt();

		default int[] nextInt(int n) {
			int[] ret = new int[n];
			for(int i = 0; i<n; i++) {
				ret[i] = nextInt();
			}
			return ret;
		}

	}

	static class Output implements Closeable, Flushable {
		public StringBuilder sb;
		public OutputStream os;
		public int BUFFER_SIZE;
		public String lineSeparator;

		public Output(OutputStream os) {
			this(os, 1<<16);
		}

		public Output(OutputStream os, int bs) {
			BUFFER_SIZE = bs;
			sb = new StringBuilder(BUFFER_SIZE);
			this.os = new BufferedOutputStream(os, 1<<17);
			lineSeparator = System.lineSeparator();
		}

		public void print(String s) {
			sb.append(s);
			if(sb.length()>BUFFER_SIZE >> 1) {
				flushToBuffer();
			}
		}

		public void println() {
			sb.append(lineSeparator);
		}

		private void flushToBuffer() {
			try {
				os.write(sb.toString().getBytes());
			}catch(IOException e) {
				e.printStackTrace();
			}
			sb = new StringBuilder(BUFFER_SIZE);
		}

		public void flush() {
			try {
				flushToBuffer();
				os.flush();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			flush();
			try {
				os.close();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

	}
}