n fish, numbered from 1 to n, live in a lake. Every day right one pair of fish meet, and the probability of each other pair meeting is the same. If two fish with indexes i and j meet, the first will eat up the second with the probability aij, and the second will eat up the first with the probability aji = 1 - aij. The described process goes on until there are at least two fish in the lake. For each fish find out the probability that it will survive to be the last in the lake.

Input

The first line contains integer n (1 ≤ n ≤ 18) — the amount of fish in the lake. Then there follow n lines with n real numbers each — matrix a. aij (0 ≤ aij ≤ 1) — the probability that fish with index i eats up fish with index j. It's guaranteed that the main diagonal contains zeros only, and for other elements the following is true: aij = 1 - aji. All real numbers are given with not more than 6 characters after the decimal point.

Output

Output n space-separated real numbers accurate to not less than 6 decimal places. Number with index i should be equal to the probability that fish with index i will survive to be the last in the lake.

Examples

Input

2
0 0.5
0.5 0


Output

0.500000 0.500000 

Input

5
0 1 1 1 1
0 0 0.5 0.5 0.5
0 0.5 0 0.5 0.5
0 0.5 0.5 0 0.5
0 0.5 0.5 0.5 0


Output

1.000000 0.000000 0.000000 0.000000 0.000000 
/*
	Author	:	Imran Khan
	Language:	Java
	
*/

import java.io.*;
import java.util.*;
public class Main
{
	public class BasicInputOutput
	{

		private StringTokenizer strtoken;
		private BufferedReader bufferReader;
		private BufferedWriter bufferWriter;
		private String delim = " \t\n\r\f";
		BasicInputOutput()
		{
			delim = " \t\n\r\f";
			initialize();
		}
		BasicInputOutput( String s )
		{
			delim = s;
			initialize();
		}
		private void initialize()
		{
			bufferReader = new BufferedReader( new InputStreamReader( System.in ));
			bufferWriter = new BufferedWriter( new PrintWriter( System.out ));
			strtoken = null;
		}
		private void checkStringTokenizer()throws IOException
		{
			if ( strtoken == null || strtoken.hasMoreTokens() == false )
				strtoken = new StringTokenizer( bufferReader.readLine(), delim );
		}
		public int getNextInt()throws IOException
		{
			checkStringTokenizer();
			return Integer.parseInt( strtoken.nextToken());
		}

		public long getNextLong()throws IOException
		{
			checkStringTokenizer();
			return Long.parseLong( strtoken.nextToken());
		}

		public double getNextDouble()throws IOException
		{
			checkStringTokenizer();
			return Double.parseDouble( strtoken.nextToken());
		}

		public float getNextFloat()throws IOException
		{
			checkStringTokenizer();
			return Float.parseFloat( strtoken.nextToken());
		}

		public String getNextString()throws IOException
		{
			checkStringTokenizer();
			return strtoken.nextToken();
		}

		public String getNextLine()throws IOException
		{
			checkStringTokenizer();
			return bufferReader.readLine();
		}

		public void skipCurrentLine()throws IOException
		{
			checkStringTokenizer();
			strtoken = null;
		}
		public void write( String var )throws IOException
		{
			bufferWriter.write( var );
		}

		public < T > void write( char sep, T... var )throws IOException
		{
			if ( var.length == 0 )
				return ;
			bufferWriter.write( var[0].toString());
			for ( int i = 1; i < var.length; i++ )
				bufferWriter.write( sep + var[i].toString());
		}

		public void flush()throws IOException
		{
			bufferWriter.flush();
		}
	}

	public static void main(String[] args)
	{
		try
		{
			new Main().run();
		}
		catch (Exception ex)
		{
			ex.printStackTrace();
		}
	}
	private BasicInputOutput iohandler;
	private int n;
	private double[][] mat;
	private double[][] sum;
	private double[] dp;
	private int tolive;
	private void run()throws Exception
	{
		initialize();
		solve();
	}
	private void initialize() throws Exception
	{
		iohandler=new BasicInputOutput();
		n=iohandler.getNextInt();
		mat=new double[n][n];
		sum=new double[(1<<n)+10][n];
		dp=new double[1<<n];
		for(int i=0;i<n;i++) for(int j=0;j<n;j++)
		{
			mat[i][j]=iohandler.getNextDouble();
		}
	}
	private int bitCount(int mask)
	{
		int ret=0;
		while(mask>0) {
			ret++;
			mask&=(mask-1);
		}
		return ret;
	}
	private void solve() throws Exception
	{
		double[] ans=new double[n];
		int ub=1<<n;
		for(int i=1;i<ub;i++) {
			for(int j=0;j<n;j++) {
				sum[i][j]=0;
				for(int k=0;k<n;k++) if ((i&(1<<k))!=0) sum[i][j]+=mat[k][j];
				int cntbit=bitCount(i);
				if (cntbit>1)
				sum[i][j]/=((double)cntbit*(cntbit-1.))/2.;
			}
		}
		for(int i=0;i<n;i++)
		{
			for(int mask=1;mask<ub;mask++) {
				dp[mask]=0;
				if ((mask&(1<<i))==0) continue;
				if (bitCount(mask)==1)
				{
					dp[mask]=1.;
				} else
				for(int k=0;k<n;k++) {
					if ((mask&(1<<k))==0) continue;
					if (i==k) continue;
					dp[mask]+=sum[mask][k]*dp[mask-(1<<k)];
				}
			}
			ans[i]=dp[ub-1];
		}
		iohandler.write(ans[0]+"");
		for(int i=1;i<n;i++) iohandler.write(" "+ans[i]);
		iohandler.write("\n");
		iohandler.flush();
	}
}
