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.awt.Point;
import java.io.*;
import java.math.BigInteger;
import java.util.*;
import static java.lang.Math.*;

public class ProblemE_16 {
    
    final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE")!=null;
    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok = new StringTokenizer("");
    
    void init() throws FileNotFoundException{
        if (ONLINE_JUDGE){
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }else{
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        }
    }
    
    String readString() throws IOException{
        while(!tok.hasMoreTokens()){
            tok = new StringTokenizer(in.readLine());
        }
        return tok.nextToken();
    }
    
    int readInt() throws IOException{
        return Integer.parseInt(readString());
    }
    
    long readLong() throws IOException{
        return Long.parseLong(readString());
    }
    
    double readDouble() throws IOException{
        return Double.parseDouble(readString());
    }
    
    public static void main(String[] args){
        new ProblemE_16().run();
    }
    
    public void run(){
        try{
            long t1 = System.currentTimeMillis();
            init();
            solve();
            out.close();
            long t2 = System.currentTimeMillis();
            System.err.println("Time = "+(t2-t1));
        }catch (Exception e){
            e.printStackTrace(System.err);
            System.exit(-1);
        }
    }
    
    void solve() throws IOException{
        int n = readInt();
        double[][] a = new double[n][n];
        for (int i = 0; i < n; i++){
            for (int j = 0; j < n; j++){
                a[i][j] = readDouble();
            }
        }
        double[] d = new double[1<<n];
        d[(1 << n) - 1] = 1;
        for (int i = (1 << n) - 1; i > 0; i--){
            ArrayList<Integer> list = new ArrayList<Integer>();
            for (int j = 0; j < n; j++){
                if ((i & (1 << j)) != 0) list.add(j);
            }
            double s = 0;
            for (int j = 0; j < list.size(); j++){
                s = 0;
                for (int k = 0; k < list.size(); k++){
                    s += a[list.get(k)][list.get(j)];
                }
                d[i ^ (1 << list.get(j))] += s * d[i] * 2 / list.size() / (list.size() - 1);
            }
        }
        for (int i = 0; i < n; i++){
            out.printf(Locale.US, "%.9f", d[1 << i]);
            out.print(" ");
        }
    }
    
    static int[][] step8 = {{-1, 0}, {1, 0}, {0, -1}, {0, 1}, {-1, -1}, {1, -1}, {-1, 1}, {1, 1}};
    
    static int[][] stepKnight = {{-2, -1}, {-2, 1}, {-1, -2}, {-1, 2}, {1, -2}, {1, 2}, {2, -1}, {2, 1}};
    
    static long gcd(long a, long b){
        if (a == 0) return b;
        return gcd(b % a, a);
    }
    
    static long lcm(long a, long b){
        return a / gcd(a, b)*b;
    }

    static long[] gcdPlus(long a, long b){
        long[] d = new long[3];
        if (a == 0){
            d[0] = b;
            d[1] = 0;
            d[2] = 1;
        }else{
            d = gcdPlus(b % a, a);
            long r = d[1];
            d[1] = d[2] - b/a*d[1];
            d[2] = r;
        }
        return d;
    }
    
    static long binpow(long a, int n){
        if (n == 0) return 1;
        if ((n & 1) == 0){
            long b = binpow(a, n/2);
            return b*b;
        }else return binpow(a, n - 1)*a;
    }
    
    static long binpowmod(long a, int n, long m){
        if (m == 1) return 0;
        if (n == 0) return 1;
        if ((n & 1) == 0){
            long b = binpowmod(a, n/2, m);
            return (b*b) % m;
        }else return binpowmod(a, n - 1, m)*a % m;
    }
    
    static long phi(long n){
        int[] p = Sieve((int)ceil(sqrt(n)) + 2);
        long phi = 1;
        for (int i = 0; i < p.length; i++){
            long x = 1;
            while (n % p[i] == 0){
                n /= p[i];
                x *= p[i];
            }
            phi *= x - x/p[i];
        }
        if (n != 1) phi *= n - 1;
        return phi;
    }
    
    static long f(long n, int x, int k){ //Кол-во десятичных чисел (включая 0), содержащих в себе цифры от 0 до k-1
        if (n == 0) return 1;
        long b = binpow(10, x - 1);
        long c = n / b;
        return (c < k? c: k)*binpow(k, x - 1) + (c < k? 1: 0)*f(n % b, x - 1, k);
    }
    
    static long fib(int n){
        if (n == 0) return 0;
        if ((n & 1) == 0){
            long f1 = fib(n/2 - 1);
            long f2 = fib(n/2 + 1);
            return f2*f2 - f1*f1;
        }else{
            long f1 = fib(n/2);
            long f2 = fib(n/2 + 1);
            return f1*f1 + f2*f2;
        }
    }
    
    static BigInteger BigFib(int n){
        if (n == 0) return BigInteger.ZERO;
        if ((n & 1) == 0){
            BigInteger f1 = BigFib(n/2 - 1);
            f1 = f1.multiply(f1);
            BigInteger f2 = BigFib(n/2 + 1);
            f2 = f2.multiply(f2);
            return f2.subtract(f1);
        }else{
            BigInteger f1 = BigFib(n/2);
            f1 = f1.multiply(f1);
            BigInteger f2 = BigFib(n/2 + 1);
            f2 = f2.multiply(f2);
            return f2.add(f1);
        }
    }
    
    static public class PointD{
        
        double x, y;
        
        public PointD(double x, double y){
            this.x = x;
            this.y = y;
        }
    }
    
    static double d(Point p1, Point p2){
        return sqrt(d2(p1, p2));
    }
    
    static public double d(PointD p1, PointD p2){
        return sqrt(d2(p1, p2));
    }
    
    static double d2(Point p1, Point p2){
        return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
    }
    
    static public double d2(PointD p1, PointD p2){
        return (p1.x - p2.x) * (p1.x - p2.x) + (p1.y - p2.y) * (p1.y - p2.y);
    }
    
    static boolean IsProbablyPrime(long n){
        if (n == 1) return false;
        if ((n & 1) == 0) return false;
        for (int j = 3; j < sqrt(n) + 1; j += 2){
            if (n % j == 0) return false;
        }
        return true;
    }

    static int[] Sieve(int n){
        boolean[] b = new boolean[n+1];
        Arrays.fill(b, true);
        b[0] = false;
        b[1] = false;
        long nLong = n;
        int j=0;
        for (int i = 1; i <= n; i++) {
            if (b[i]){
                j++;
                if (((long)i)*i <= nLong) {
                    for (int k = i*i; k <= n; k += i) {
                        b[k] = false;
                    }
                }
            }
        }
        int[] p = new int[j];
        Arrays.fill(p, 0);
        j=0;
        for (int i = 2; i <= n; i++) {
            if (b[i]){
                p[j]=i;
                j++;
            }
        }
        return p;
    }
    
    static int[][] Palindromes(String s){
        char[] c = s.toCharArray();
        int n = c.length;
        int[][] d = new int[2][n];
        int l = 0, r = -1;
        for (int i = 0; i < n; i++){
            int j = (i > r? 0: min(d[0][l+r-i+1], r-i+1)) + 1;
            for (; i - j >= 0 && i + j - 1< n && c[i-j] == c[i+j-1]; j++);
            d[0][i] = --j;
            if (i + d[0][i] - 1 > r){
                r = i + d[0][i] - 1;
                l = i - d[0][i];
            }
        }
        l = 0;
        r = -1;
        for (int i = 0; i < n; i++){
            int j = (i > r? 0: min(d[1][l+r-i], r-i)) + 1;
            for (; i - j >= 0 && i + j < n && c[i-j] == c[i+j]; j++);
            d[1][i] = --j;
            if (i + d[1][i] > r){
                r = i + d[1][i];
                l = i - d[1][i];
            }
        }
        return d;
    }
    
    static public class Permutation {
        
        int[] a;
        int n;
        
        public Permutation(int n){
            this.n=n;
            a=new int[n];
            for (int i=0; i<n; i++){
                a[i]=i;
            }
        }
        
        public boolean nextPermutation(){ //Пишется с do{}while(nextPermutation(a));
            int i=n-1;
            for (i=n-2; i>=0; i--){
                if (a[i]<a[i+1]){
                    break;
                }
            }
            if (i==-1){
                return false;
            }
            int jMin=i+1;
            for (int j=n-1; j>i; j--){
                if (a[i]<a[j]&&a[j]<a[jMin]){
                    jMin=j;
                }
            }
            swap(i, jMin);
            for (int j=1; j<=(n-i)/2; j++){
                swap(i+j, n-j);
            }
            return true;
        }
        
        
        public int get(int i){
            return a[i];
        }
        
        void swap(int i, int j){
            int r=a[i];
            a[i]=a[j];
            a[j]=r;
        }
    }
    
    static public class Fraction implements Comparable<Fraction>, Cloneable{
        
        public final Fraction FRACTION_ZERO = new Fraction();
        public final Fraction FRACTION_ONE = new Fraction(1);
        public long numerator = 0;
        public long denominator = 1;
        
        public Fraction(){
            numerator = 0;
            denominator = 1;
        }
        
        public Fraction(long numerator){
            this.numerator = numerator;
            denominator = 1;
        }
        
        public Fraction(long numerator, long denominator){
            this.numerator = numerator;
            this.denominator = denominator;
            Cancellation();
        }
        
        public Fraction(double numerator, double denominator, int accuracy){
            this.numerator = (long)(numerator*pow(10,accuracy));
            this.denominator = (long)(denominator*pow(10,accuracy));
            Cancellation();
        }
        
        public Fraction(String s){
            if (s.charAt(0) == '-'){
                denominator = -1;
                s = s.substring(1);
            }
            if (s.indexOf("/") != -1){
                denominator *= Integer.parseInt(s.substring(s.indexOf("/") + 1));
            }
            if (s.indexOf(" ") != -1){
                numerator = Integer.parseInt(s.substring(0, s.indexOf(" "))) * abs(denominator) + Integer.parseInt(s.substring(s.indexOf(" ") + 1, s.indexOf("/")));
            }else{
                if (s.indexOf("/") != -1){
                    numerator = Integer.parseInt(s.substring(0, s.indexOf("/")));
                }else{
                    numerator = Integer.parseInt(s)*abs(denominator);
                }
            }
            this.Cancellation();
        }
        
        void Cancellation(){
            long g = gcd(abs(numerator), abs(denominator));
            numerator /= g;
            denominator /= g;
            if (denominator < 0){
                numerator *= -1;
                denominator *= -1;
            }
        }
        
        public String toString(){
            String s = "";
            if (numerator == 0){
                return "0";
            }
            if (numerator < 0){
                s += "-";
            }
            if (abs(numerator) >= denominator){
                s += Long.toString(abs(numerator) / denominator) + " ";
            }
            if (abs(numerator) % denominator != 0){
                s += Long.toString(abs(numerator) % denominator);
            }else{
                s = s.substring(0, s.length()-1);
            }
            if (denominator != 1){
                s += "/" + Long.toString(denominator);
            }
            return s;
        }
        
        public Fraction add(Fraction f){
            Fraction fResult = new Fraction();
            fResult.denominator = lcm(denominator, f.denominator);
            fResult.numerator = numerator * fResult.denominator / denominator + f.numerator * fResult.denominator / f.denominator;
            fResult.Cancellation();
            return fResult;
        }
        
        public Fraction subtract(Fraction f){
            Fraction fResult = new Fraction();
            fResult.denominator = lcm(denominator, f.denominator);
            fResult.numerator = numerator * fResult.denominator / denominator - f.numerator * fResult.denominator / f.denominator;
            fResult.Cancellation();
            return fResult;
        }
        
        public Fraction multiply(Fraction f){
            Fraction fResult = new Fraction();
            fResult.numerator = numerator * f.numerator;
            fResult.denominator = denominator * f.denominator;
            fResult.Cancellation();
            return fResult;
        }
        
        public Fraction divide(Fraction f){
            Fraction fResult = new Fraction();
            fResult.numerator = numerator * f.denominator;
            fResult.denominator = denominator * f.numerator;
            fResult.Cancellation();
            return fResult;
        }
        
        @Override
        public int compareTo(Fraction f){
            long g = gcd(denominator, f.denominator);
            long res = numerator * (f.denominator / g) - f.numerator * (denominator / g);
            if (res < 0){
                return -1;
            }
            if (res > 0){
                return 1;
            }
            return 0;
        }
        
        public Fraction clone(){
            Fraction fResult = new Fraction(numerator, denominator);
            return fResult;
        }
        
        public Fraction floor(){
            Fraction fResult = this.clone();
            fResult.numerator = (fResult.numerator / fResult.denominator) * fResult.denominator;
            return fResult;
        }
        
        public Fraction ceil(){
            Fraction fResult = this.clone();
            fResult.numerator = (fResult.numerator/fResult.denominator + 1) * fResult.denominator;
            return fResult;
        }
        
        public Fraction binpow(int n){
            if (n==0) return FRACTION_ONE;
            if ((n&1)==0){
                Fraction f=this.binpow(n/2);
                return f.multiply(f);
            }else return binpow(n-1).multiply(this);
        }
    }
    
    static public class FenwickTree_1{  //One-dimensional array     
        
        int n;
        long[] t;
        
        public FenwickTree_1(int n){
            this.n = n;
            t = new long[n];
        }
        
        public long sum(int xl, int xr){
            return sum(xr) - sum(xl);
        }
        
        public long sum(int x){
            long result = 0;
            for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
                result += t[i];
            }
            return result;
        }
        
        public void update(int x, long delta){
            for (int i = x; i < n; i = (i | (i + 1))){
                t[i] += delta;
            }
        }
    }
    
    static public class FenwickTree_2{  //Two-dimensional array
        
        int n, m;
        long[][] t;
        
        public FenwickTree_2(int n, int m){
            this.n = n;
            this.m = m;
            t = new long[n][m];
        }
        
        public long sum(int xl, int yl, int xr, int yr){
            return sum(xr, yr) - sum(xl - 1, yr) - sum(xr, yl - 1) + sum(xl - 1, yl - 1);
        }
        
        public long sum(int x, int y){
            long result = 0;
            for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
                for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
                    result+=t[i][j];
                }
            }
            return result;
        }
        
        public void update(int x, int y, long delta){
            for (int i = x; i < n; i = (i | (i + 1))){
                for (int j = y; j < m; j = (j | (j + 1))){
                    t[i][j] += delta;
                }
            }
        }
    }
    
    static public class FenwickTree_3{  //Three-dimensional array
        
        int n, m, l;
        long[][][] t;
        
        public FenwickTree_3(int n, int m, int l){
            this.n = n;
            this.m = m;
            this.l = l;
            t = new long[n][m][l];
        }
        
        public long sum(int xl, int yl, int zl, int xr, int yr, int zr){
            return sum(xr, yr, zr) - sum(xl - 1, yr, zr)
            + sum(xl - 1, yr, zl - 1) - sum(xr, yr, zl - 1)
            - sum(xr, yl - 1, zr) + sum(xl - 1, yl - 1, zr)
            - sum(xl - 1, yl - 1, zl - 1) + sum(xr, yl - 1, zl - 1);
        }
        
        public long sum(int x, int y, int z){
            long result = 0;
            for (int i = x; i >= 0; i = (i & (i + 1)) - 1){
                for (int j = y; j >= 0; j = (j & (j + 1)) - 1){
                    for (int k = z; k >= 0; k = (k & (k + 1)) - 1){
                        result += t[i][j][k];
                    }
                }
            }
            return result;
        }
        
        public void update(int x, int y, int z, long delta){
            for (int i = x; i < n; i = (i | (i + 1))){
                for (int j = y; j < n; j = (j | (j + 1))){
                    for (int k = z; k < n; k = (k | (k + 1))){
                        t[i][j][k] += delta;
                    }
                }
            }
        }
    }
}

