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 javafx.scene.layout.Priority;
import java.io.*;
import java.lang.reflect.Array;
import java.net.Inet4Address;
import java.util.*;
import java.lang.*;
import java.util.HashMap;
import java.util.PriorityQueue;
public class templ implements Runnable{
    static class pair implements Comparable
    {
        int f;
        int s;
        pair(int fi,int se)
        {
            f=fi;
            s=se;
        }
        public int compareTo(Object o)
        {
            pair pr=(pair)o;
            if(s>pr.s)
                return 1;
            if(s==pr.s)
            {
                if(f>pr.f)
                    return 1;
                else
                    return -1;
            }
            else
                return -1;
        }
        public boolean equals(Object o)
        {
            pair ob=(pair)o;
            int ff;
            int ss;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                if((ff==this.f)&&(ss==this.s))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s).hashCode();
        }
    }
    public class triplet implements Comparable
    {
        int f,t;
        int s;
        triplet(int f,int s,int t)
        {
            this.f=f;
            this.s=s;
            this.t=t;
        }
        public boolean equals(Object o)
        {
            triplet ob=(triplet)o;
            int ff;
            int ss;
            int tt;
            if(o!=null)
            {
                ff=ob.f;
                ss=ob.s;
                tt=ob.t;
                if((ff==this.f)&&(ss==this.s)&&(tt==this.t))
                    return true;
            }
            return false;
        }
        public int hashCode()
        {
            return (this.f+" "+this.s+" "+this.t).hashCode();
        }
        public int compareTo(Object o)
        {
            triplet tr=(triplet)o;
            if(t>tr.t)
                return 1;
            else
                return -1;
        }
    }
    int n,a[],dp[][],masks[];
    int prime[]={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53};
    HashMap<Integer,Integer>hm=new HashMap<>();
    int m[][];
    int solve(int i,int mask)
    {
        if(i==n+1)
            return 0;
        if(dp[i][mask]!=-1)
            return dp[i][mask];
        if(a[i]==1)
        {
            dp[i][mask] = solve(i + 1, mask);
            m[i][mask]=1;
        }
        else
        {
            dp[i][mask]=a[i]-1+solve(i+1,mask);
            m[i][mask]=1;
            for(int j=2;j<=2*a[i]-2;j++)
            {
                if((mask & masks[j])==0)
                {
                    int z=Math.abs(j - a[i]) + solve(i + 1, (mask|masks[j]));
                    if(dp[i][mask]>z)
                    {
                        dp[i][mask]=z;
                        m[i][mask]=j;
                    }
                }
            }
        }
        return dp[i][mask];
    }
    public static void main(String args[])throws Exception
    {
        new Thread(null,new templ(),"templ",1<<27).start();
    }
    public void run()
    {
        try
        {
            InputReader in = new InputReader(System.in);
            PrintWriter out = new PrintWriter(System.out);
            n=in.ni();
            a=new int[n+1];
            masks=new int[60];
            for(int i=1;i<=n;i++)
                a[i]=in.ni();
            dp=new int[n+1][1<<16];
            m=new int[n+1][1<<16];
            for(int i=0;i<=n;i++)
            {
                Arrays.fill(dp[i],-1);
            }
            for(int i=0;i<16;i++)
                hm.put(prime[i],i);
            for(int i=2;i<59;i++)
            {
                for(int j=2;j<=i;j++)
                {
                    //System.out.println(j);
                    if(i%j==0&&hm.containsKey(j))
                    {
                        masks[i] = (masks[i] | (1 << hm.get(j)));
                    }
                }
            }
            int min=solve(1,0);
            int mask=0;
            int i=1;
            while(i<=n)
            {
                out.print(m[i][mask]+" ");
                mask=(mask|masks[m[i][mask]]);
                i++;
            }
            out.close();
        }
        catch(Exception e){
            return;
        }
    }
    static class InputReader {

        private final InputStream stream;
        private final byte[] buf = new byte[8192];
        private int curChar, snumChars;

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

        public int read() {
            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 ni() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            int res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nl() {
            int c = read();
            while (isSpaceChar(c)) {
                c = read();
            }
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = read();
            }
            long res = 0;
            do {
                res *= 10;
                res += c - '0';
                c = read();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public int[] nextIntArray(int n) {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

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

        public String nextLine() {
            int c = read();
            while (isSpaceChar(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndOfLine(c));
            return res.toString();
        }

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

        private boolean isEndOfLine(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

    }
}