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.OutputStreamWriter;
import java.io.BufferedWriter;
import java.util.Locale;
import java.io.OutputStream;
import java.io.PrintWriter;
import java.util.AbstractList;
import java.io.Writer;
import java.util.Collection;
import java.util.List;
import java.io.IOException;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 * @author Jacob Jiang
 */
public class Main {
	public static void main(String[] args) {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		OutputWriter out = new OutputWriter(outputStream);
		TaskE solver = new TaskE();
		solver.solve(1, in, out);
		out.close();
	}
}

class TaskE {
    public void solve(int testNumber, InputReader in, OutputWriter out) {
        int n = in.nextInt();
        double[][] probability = in.next2DDoubleArray(n, n);
        double[] dp = new double[1 << n];
        dp[dp.length - 1] = 1;
        for (int mask = (1 << n) - 1; mask >= 0; mask--) {
            int count = Integer.bitCount(mask);
            if (count <= 1) continue;
            double multi = 1. / calc(count);
            for (int i = 0; i < n; i++) {
                if (NumberUtils.checkBit(mask, i)) {
                    for (int j = i + 1; j < n; j++) {
                        if (NumberUtils.checkBit(mask, j)) {
                            // i eat j
                            dp[mask - (1 << j)] += multi * probability[i][j] * dp[mask];
                            // j eat i
                            dp[mask - (1 << i)] += multi * probability[j][i] * dp[mask];
                        }
                    }
                }
            }
        }
        double[] answer = new double[n];
        for (int i = 0; i < n; i++) {
            answer[i] = dp[1 << i];
        }
        out.printLine(ArrayUtils.asList(answer).toArray());
    }

    private static int calc(int x) {
        return x * (x - 1) / 2;
    }
}

class InputReader {

    private InputStream stream;
    private byte[] buf = new byte[1024];
    private int curChar;
    private int numChars;

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

    public int read() {
        if (numChars == -1)
            throw new InputMismatchException();
        if (curChar >= numChars) {
            curChar = 0;
            try {
                numChars = stream.read(buf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (numChars <= 0)
                return -1;
        }
        return buf[curChar++];
    }

    public int nextInt() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        int res = 0;
        do {
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c & 15;
            c = read();
        } while (!isSpaceChar(c));
        return res * sgn;
    }

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

    public double nextDouble() {
        int c = read();
        while (isSpaceChar(c))
            c = read();
        int sgn = 1;
        if (c == '-') {
            sgn = -1;
            c = read();
        }
        double res = 0;
        while (!isSpaceChar(c) && c != '.') {
            if (c == 'e' || c == 'E')
                return res * Math.pow(10, nextInt());
            if (c < '0' || c > '9')
                throw new InputMismatchException();
            res *= 10;
            res += c - '0';
            c = read();
        }
        if (c == '.') {
            c = read();
            double m = 1;
            while (!isSpaceChar(c)) {
                if (c == 'e' || c == 'E')
                    return res * Math.pow(10, nextInt());
                if (c < '0' || c > '9')
                    throw new InputMismatchException();
                m /= 10;
                res += (c - '0') * m;
                c = read();
            }
        }
        return res * sgn;
    }

    public double[] nextDoubleArray(int count) {
        double[] result = new double[count];
        for (int i = 0; i < count; i++) {
            result[i] = nextDouble();
        }
        return result;
    }

    public double[][] next2DDoubleArray(int n, int m) {
        double[][] result = new double[n][];
        for (int i = 0; i < n; i++) {
            result[i] = nextDoubleArray(m);
        }
        return result;
    }

    }

class OutputWriter {
    PrintWriter writer;

    public OutputWriter(OutputStream stream) {
        writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(stream)));
    }

    public OutputWriter(Writer writer) {
        this.writer = new PrintWriter(writer);
    }

    public void print(Object obj) {
        writer.print(obj);
    }

    public void println() {
        writer.println();
    }

    public void print(char c) {
        writer.print(c);
    }

    public void close() {
        writer.close();
    }

    public void printItems(Object... items) {
        for (int i = 0; i < items.length; i++) {
            if (i != 0) {
                print(' ');
            }
            print(items[i]);
        }
    }

    public void printLine(Object... items) {
        printItems(items);
        println();
    }

}

class NumberUtils {

    public static boolean checkBit(int mask, int bit) {
        return (mask & (1 << bit)) != 0;
    }

    }

class ArrayUtils {

    private ArrayUtils() {
    }

    public static List<Double> asList(double[] array) {
        return new DoubleList(array);
    }

    private static class DoubleList extends AbstractList<Double> {
        double[] array;

        private DoubleList(double[] array) {
            this.array = array;
        }

        public Double set(int index, Double element) {
            double result = array[index];
            array[index] = element;
            return result;
        }

        public Double get(int index) {
            return array[index];
        }

        public int size() {
            return array.length;
        }
    }

    }

