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 
import java.io.*;
import java.text.DecimalFormat;

public class ProblemD {

    private double survive(int round, int set) {
        if (sur[round][set] >= 0)
            return sur[round][set];
        double res = 0.0;
        int count = 0;
        for(int i=0;i<n;i++) {

            if ((set & (1 << i)) > 0) {
                double res2 = 0.0;
                for(int j=0;j<n;j++)
                    if ((set & (1 << j)) == 0) {
                        res2 += survive(round - 1, set + (1 << j)) * a[i][j];
                        count++;
                    }
                res += res2;
            }

        }
        count = (n-round+1) * (n - round) / 2;
        sur[round][set] = res / count;
        return sur[round][set];
    }

    int n;
    double[][] a, sur;

    public void solve() {
        boolean oj = true;

        try {
            Reader reader = oj ? new InputStreamReader(System.in) : new FileReader("inputD.txt");
            Writer writer = oj ? new OutputStreamWriter(System.out) : new FileWriter("outputD.txt");
            BufferedReader br = new BufferedReader(reader);
            PrintWriter out = new PrintWriter(writer);

            MyTokenizer tok = new MyTokenizer(br.readLine());
            n = (int)tok.getNum();
            a = new double[n][n];

            int all = (1 << n) - 1;

            sur = new double[n][all + 1];
            for(int i=0;i<n;i++) {
                tok = new MyTokenizer(br.readLine());
                for(int j=0;j<n;j++) {
                    a[i][j] = tok.getNum();
                }
                for(int j=0;j<=all;j++)
                    sur[i][j] = -1;
            }

            DecimalFormat format = new DecimalFormat("0.000000");

            sur[0][all] = 1;
            double[] res = new double[n];
            for(int i=0;i<n;i++) {
                res[i] = survive(n - 1, 1 << i);
                String sres = format.format(res[i]).replace(',','.');
                out.printf("%s ", sres);
            }

            br.close();
            out.close();
            reader.close();
            writer.close();
        }
        catch (Exception ex) {
            ex.printStackTrace();
        }
        finally {
        }
    }

    public static void main(String[] args) {
        ProblemD f = new ProblemD();
        f.solve();
    }

    private class MyTokenizer {
        private String s;
        private int cur;

        public MyTokenizer(String s) {
            this.s = s;
            cur = 0;
        }

        public void skip() {
            while (cur < s.length() && (s.charAt(cur) == ' ' || s.charAt(cur) == '\n')) {
                cur++;
            }
        }

        public double getNum() {
            skip();
            String snum = "";
            while (cur < s.length() && (s.charAt(cur) >= '0' && s.charAt(cur) <= '9' || s.charAt(cur) == '.')) {
                snum += s.charAt(cur);
                cur++;
            }
            return Double.valueOf(snum);
        }

        public String getString() {
            skip();
            String s2 = "";
            while (cur < s.length() && (s.charAt(cur) >= 'a' && s.charAt(cur) <= 'z')) {
                s2 += s.charAt(cur);
                cur++;
            }
            return s2;
        }

        public char getCurrentChar() throws Exception {
            if (cur < s.length())
                return s.charAt(cur);
            else
                throw new Exception("Current character out of string length");
        }

        public void moveNextChar() {
            if (cur < s.length())
                cur++;
        }

        public boolean isFinished() {
            return cur >= s.length();
        }
    }
}
