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:
//package round259;
import java.io.ByteArrayInputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.InputMismatchException;

public class B {
	InputStream is;
	PrintWriter out;
	String INPUT = "";
	
	void solve()
	{
		int n = ni();
		int[] a = na(n);
		for(int p = 0, q = n-1;p < q;p++,q--){
			int d = a[p]; a[p] = a[q]; a[q] = d;
		}
		
		int[] primes = sieveEratosthenes(58);
		int m = primes.length;
		int[][] dp = new int[n+1][1<<m];
		int[][] prev = new int[n+1][1<<m];
		for(int i = 0;i < n+1;i++){
			Arrays.fill(dp[i], 9999999);
			Arrays.fill(prev[i], -1);
		}
		dp[0][0] = 0;
		
		int[] ptn = new int[59];
		for(int d = 1;d <= 58;d++){
			int x = d;
			for(int j = 0;j < primes.length;j++){
				int p = primes[j];
				while(x % p == 0){
					x /= p;
					ptn[d] |= 1<<j;
				}
			}
		}
		
		for(int i = 0;i < n;i++){
			for(int k = 1;k <= 58;k++){
				int mask = ~ptn[k]&(1<<m)-1;
				for(int j = mask;j >= 0;j--){ j &= mask;
					int v = dp[i][j] + Math.abs(k-a[i]);
					if(v < dp[i+1][j|ptn[k]]){
						dp[i+1][j|ptn[k]] = v;
						prev[i+1][j|ptn[k]] = k;
					}
				} // include j=0
			}
		}
//		for(int i = 0;i < n;i++){
//			for(int j = 0;j < 1<<m;j++){
//				for(int k = 1;k <= 58;k++){
//					if((j&ptn[k]) == 0){
//						int v = dp[i][j] + Math.abs(k-a[i]);
//						if(v < dp[i+1][j|ptn[k]]){
//							dp[i+1][j|ptn[k]] = v;
//							prev[i+1][j|ptn[k]] = k;
//						}
//					}
//				}
//			}
//		}
		
		int min = 9999999;
		int minj = -1;
		for(int j = 0;j < 1<<m;j++){
			if(dp[n][j] < min){
				min = dp[n][j];
				minj = j;
			}
		}
		for(int i = n;i >= 1;i--){
			int x = prev[i][minj];
			out.print(x + " ");
			minj ^= ptn[x];
		}
		out.println();
	}
	
	public static int[] sieveEratosthenes(int n) {
		if(n <= 32){
			int[] primes = { 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
			for(int i = 0;i < primes.length;i++){
				if(n < primes[i]){
					return Arrays.copyOf(primes, i);
				}
			}
			return primes;
		}

		int u = n + 32;
		double lu = Math.log(u);
		int[] ret = new int[(int) (u / lu + u / lu / lu * 1.5)];
		ret[0] = 2;
		int pos = 1;

		int[] isp = new int[(n + 1) / 32 / 2 + 1];
		int sup = (n + 1) / 32 / 2 + 1;

		int[] tprimes = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31 };
		for(int tp : tprimes){
			ret[pos++] = tp;
			int[] ptn = new int[tp];
			for(int i = (tp - 3) / 2;i < tp << 5;i += tp)
				ptn[i >> 5] |= 1 << (i & 31);
			for(int i = 0;i < tp;i++){
				for(int j = i;j < sup;j += tp)
					isp[j] |= ptn[i];
			}
		}

		// 3,5,7
		// 2x+3=n
		int[] magic = { 0, 1, 23, 2, 29, 24, 19, 3, 30, 27, 25, 11, 20, 8, 4,
				13, 31, 22, 28, 18, 26, 10, 7, 12, 21, 17, 9, 6, 16, 5, 15, 14 };
		int h = n / 2;
		for(int i = 0;i < sup;i++){
			for(int j = ~isp[i];j != 0;j &= j - 1){
				int pp = i << 5 | magic[(j & -j) * 0x076be629 >>> 27];
				int p = 2 * pp + 3;
				if(p > n)
					break;
				ret[pos++] = p;
				for(int q = pp;q <= h;q += p)
					isp[q >> 5] |= 1 << (q & 31);
			}
		}

		return Arrays.copyOf(ret, pos);
	}
	
	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new PrintWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new B().run(); }
	
	private byte[] inbuf = new byte[1024];
	private int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}
	
	private char[][] nm(int n, int m)
	{
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}
	
	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}
	
	private int ni()
	{
		int num = 0, b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}
		
		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}
	
	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}