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.util.*;

public class HarmonyChest {
	static int n;
	static int[] a;
	static int[] primes={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,57,59};
	static int[] masks;
	public static void main(String[] args) {
		Scanner scan=new Scanner(System.in);
		n=scan.nextInt();
		a=new int[n];
		for(int i=0;i<n;i++) a[i]=scan.nextInt();
		ans=new int[n];
		dp=new int[n][1<<18];
		for(int i=0;i<n;i++) Arrays.fill(dp[i],-1);
		masks=new int[60];
		for(int i=1;i<60;i++) {
			int mask=0;
			for(int j=0;j<primes.length;j++) {
				if(i%primes[j]==0) mask|=(1<<j);
			}
			masks[i]=mask;
		}
//		long begin=System.currentTimeMillis();
		genSeq(0,0,go(0,0));
//		System.out.println(System.currentTimeMillis()-begin);
	}
	public static void genSeq(int at, int mask, int dif) {
		if(at==n) return;
		for(int nxt=1;nxt<60;nxt++) {
			if((mask&masks[nxt])>0) continue;//factor already used
			if(dif-Math.abs(a[at]-nxt)==go(at+1,mask|masks[nxt])) {
				//answer is consistent with the next state so you can go on;)
				System.out.print(nxt+" ");
				genSeq(at+1,mask|masks[nxt],dif-Math.abs(a[at]-nxt));
				return;//return bc u have an answer now
			}
		}
	}
	static int[] ans;
	static int[][] dp;
	
	public static int go(int at, int mask) {
		if(at==n) return 0;
		if(dp[at][mask]!=-1) return dp[at][mask];
		int res=Integer.MAX_VALUE;
		for(int nxt=1;nxt<60;nxt++) {
			if((mask&masks[nxt])>0) continue;
			res=Math.min(res,Math.abs(a[at]-nxt)+go(at+1,mask|masks[nxt]));
		}
		return dp[at][mask]=res;
	}
}