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.util.*;
import java.util.regex.Matcher;

public class Main {

    public static void main(String[] args) throws IOException {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = /*new InputReader(new FileReader("input.txt"));*/   new InputReader(inputStream);
        PrintWriter out = /*new PrintWriter("output.txt"); */  new PrintWriter(outputStream);
        TaskB solver = new TaskB();
        solver.solve(in, out);
        out.close();
    }

    private static class TaskB {

        static final double EPS = 0.000000001;
        static final long MOD = 1000000007;
        List<Integer>[] adj;
        int dp[], deg[], longPath;
        boolean F[];

        void solve(InputReader in, PrintWriter out) throws IOException {


            int N = in.nextInt();
            double P[][] = new double[N][N];
            double dp[] = new double[1 << N];

            for (int i = 0; i < N; i++)
                for (int j = 0; j < N; j++)
                    P[i][j] = in.nextDouble();


            dp[(1 << N) - 1] = 1;
            for (int i = 1; i < N; i++) {

                for (int j = 0; j < (1 << N); j++) {
                    if (countSetBits(j) == (N - i)) {
                        double pAll = 0;
                        int n = N - i + 1;
                        for (int k = 0; k < N; k++) {
                            double p = 0;
                            int value = j;
                            if (!isOne(value, k)) {
                                value = value | (1 << k);
                                for (int l = 0; l < N; l++)
                                    if (isOne(value, l))
                                        p += (2.0 * P[l][k]) / (n * (n - 1));
                                p *= dp[value];
                                pAll += p;
                            }
                        }
                        dp[j] = pAll;
                    }

                }

            }

            int count = 0;
            for (int i = 0; i < (1 << N); i++) {
                if (countSetBits(i) == 1) {
                    count++;
                    out.printf("%.6f", dp[i]);
                    if (count < N) out.print(" ");
                }
            }

        }


        int countSetBits(int n) {
            int count = 0;
            while (n > 0) {
                n &= (n - 1);
                count++;
            }
            return count;
        }

        boolean isOne(int n, int k) {
            return (n & 1 << k) != 0;
        }

        long gcd(long A, long B) {
            if (B == 0) return A;
            return gcd(B, A % B);
        }

        boolean isPrime(long n) {
            if (n <= 1 || n > 3 && (n % 2 == 0 || n % 3 == 0))
                return false;
            for (long i = 5, j = 2; i * i <= n; i += j, j = 6 - j)
                if (n % i == 0)
                    return false;
            return true;
        }

        boolean isEqual(double A, double B) {
            return Math.abs(A - B) < EPS;
        }

        boolean nextPer(int[] data) {
            int i = data.length - 1;
            while (i > 0 && data[i] < data[i - 1]) {
                i--;
            }
            if (i == 0) {
                return false;
            }
            int j = data.length - 1;
            while (data[j] < data[i - 1]) {
                j--;
            }
            int temp = data[i - 1];
            data[i - 1] = data[j];
            data[j] = temp;
            Arrays.sort(data, i, data.length);
            return true;
        }

        long pow(long A, long B, long MOD) {
            if (B == 0) {
                return 1;
            }
            if (B == 1) {
                return A;
            }
            long val = pow(A, B / 2, MOD);
            if (B % 2 == 0) {
                return val * val % MOD;
            } else {
                return val * (val * A % MOD) % MOD;
            }
        }

        long mod(long X, long MOD) {
            return (X % MOD + MOD) % MOD;
        }
    }

    private static class InputReader {
        StringTokenizer st;
        BufferedReader br;

        public InputReader(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public InputReader(FileReader s) throws FileNotFoundException {
            br = new BufferedReader(s);
        }

        public String next() {
            while (st == null || !st.hasMoreTokens())
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
            return st.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public String nextLine() {
            try {
                return br.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public int[] readIntArray(int n) {
            int[] ret = new int[n];
            for (int i = 0; i < n; i++) {
                ret[i] = nextInt();
            }
            return ret;
        }
    }
}