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 
//package algorithms.dp_bitMasking;

import java.io.*;
import java.util.*;

public class Fish {
    static class FastReader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public FastReader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public FastReader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[65]; // line length
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');

            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();

            do {
                ret = ret * 10 + c - '0';
            }
            while ((c = read()) >= '0' && c <= '9');

            if (c == '.') {
                while ((c = read()) >= '0' && c <= '9') {
                    ret += (c - '0') / (div *= 10);
                }
            }

            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

    static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    static FastReader f = new FastReader();
    static StringTokenizer st;
    static StringBuilder sb = new StringBuilder("");
    private static final int mod = (int) 1e9 + 7;
    static int MAX = 500005;

    static int gcd(int a, int b) {
        if (a % b == 0) {
            return b;
        }
        return gcd(b, a % b);
    }


    static long moduloInversePrime(long a) {
        long ans = modPow(a, mod - 2);
        //System.out.println("modulo inverse of " + a + " -> " + ans);
        return ans;
    }

    static long mult(long a, long b) {
        return (a * (long) b % mod);
    }

    static long modPow(long a, int step) {
        long ans = 1;
        while (step != 0) {
            if ((step & 1) != 0)
                ans = mult(ans, a);
            a = mult(a, a);
            step >>= 1;
        }
        return ans;
    }

    static long longModulus(long x, long m) {
        long d = x / m;
        return x - d * m;
    }

    static int[] inputArray(int n) throws IOException {
        int[] a = new int[n];
        st = new StringTokenizer(br.readLine());
        for (int i = 0; i < n; i++) {
            a[i] = Integer.parseInt(st.nextToken());
        }
        return a;
    }

    public static void main(String[] args) throws IOException {
        int n = f.nextInt();
        double[][] prob = new double[n][n];
        for(int i = 0 ; i < n ; i++) {
            for(int j = 0 ; j < n;  j++) {
                prob[i][j] = f.nextDouble();
            }
        }
        double[] dp = new double[1<<n];
        Arrays.fill(dp , -1);
        for (int i = 0; i < n; i++) {
            //Arrays.fill(dp , -1);
            sb.append(code(prob , n , dp , 1<<i)).append("\n");
        }
        System.out.println(sb);
    }

    static double code(double[][]prob , int n , double[] dp , int mask) {
        //System.out.println("i - " + i + " mask - " + Integer.toBinaryString(mask));

        if(mask == ((1<<n) - 1)) {
            return 1;
        }

        if(dp[mask] > -0.9) {
            return dp[mask];
        }

        int k = Integer.bitCount(mask) + 1;
        int kc2 = k * (k - 1) / 2;


        double res = 0;

        for(int j = 0 ; j < n ; j++) {
            if((mask &(1 << j)) == 0) {
                double temp = 0;
                for (int itr = 0; itr < n; itr++) {
                    if((mask & (1<<itr)) != 0) {
                        temp += prob[itr][j];
                    }
                }
                res += (temp / kc2) * code(prob , n , dp , mask | (1<<j));
                //System.out.println("i - " + i + " j - " + j + " ts[j][i] - " + ts[j][i]);
            }
        }
        dp[mask] = res;
        return res;
    }
}
/*
2
0 0.5
0.5 0

 */
