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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;
import java.math.*;
import java.text.*;
public class Main {
    InputStream is;
    PrintWriter out;
    String INPUT = "";
    //class  Declaration
 
static class pair implements Comparable < pair > {
long x;
long y;
pair(long i, long j) {
    x = i;
    y = j;
}
public int compareTo(pair p) {
    if (this.x != p.x) {
        return Long.compare(this.x,p.x);
    } else {
        return Long.compare(this.y,p.y);
    }
}
public int hashCode() {
    return (x + " " + y).hashCode();
}
public String toString() {
    return x + " " + y;
}
public boolean equals(Object o) {
    pair x = (pair) o;
    return (x.x == this.x && x.y == this.y);
}
}
 
// int[] dx = {0,0,1,-1};
// int[] dy = {1,-1,0,0};
// int[] ddx = {0,0,1,-1,1,-1,1,-1}; 
// int[] ddy = {1,-1,0,0,1,-1,-1,1};
 
int inf = (int) 1e9 + 9;
long biginf  = (long)1e18 + 7 ;
long mod =  (long)1e9+7;  
 
double[][] prob;
double[] dp ; 
int n;
void solve() throws Exception {
    n=ni();
    prob=  new double[n+1][n+1];
    for(int i=1;i<=n;++i){
        for(int j=1;j<=n;++j){
            prob[i][j]=nd();
        }
    }

    
    /*
    dp(i,A = {s}-i) =  sum of (for all j in A dp(j,A-j)* prob[i][j]/(kC2)) 
    */
    
     dp= new double[1<<n];
     Arrays.fill(dp,-1.0);

    dp[0]=1;

    
    for(int i=1;i<=n;++i){
        int mask = ((1<<n)-1)^(1<<(i-1));
        double ans = recur(mask); 
        System.out.printf("%.7f ",ans);
    }

    System.out.println("");
    //watch(dp);
    
}
double recur(int mask){
    //pn("calling "+winner+" "+mask);
    if(dp[mask]!= -1.0) return dp[mask];

    double ans = 0.0;
    int players = 1;
    for(int i=0;i<n;++i){
        if(((mask>>i)&1)==0){
            players++;

        }
    }
    double denom = (players*(players-1)*1.0)/2.0;
    for(int i=0;i<n;++i){
        if(((mask>>i)&1)==1){
            int newMask = mask^(1<<i);
            double sum =0;
            for(int j=0;j<n;++j){
                if(((mask>>j)&1)==0){
                    sum+= prob[j+1][i+1];
                }
            }
            ans += recur(newMask)*(sum/denom);

            
        }
    }
    return dp[mask] = ans ;
   
}

long pow(long a, long b) {
    long result = 1;
    while (b > 0) {
        if (b % 2 == 1) result = (result * a) % mod;
        b /= 2;
        a = (a * a) % mod;
    }
    return result;
}
 
void print(Object o) {
        System.out.println(o);
        System.out.flush();
}
long gcd(long a, long b) {
        if (b == 0)
            return a;
        return gcd(b, a % b);
    }
void run() throws Exception {
        is = INPUT.isEmpty() ? System.in : new ByteArrayInputStream(INPUT.getBytes());
        out = new PrintWriter(System.out);
 
        long s = System.currentTimeMillis();
        solve();
        out.flush();
        //System.out.println(System.currentTimeMillis() - s + "ms");
        if (!INPUT.isEmpty()) tr(System.currentTimeMillis() - s + "ms");
    }
 
 
public static void main(String[] args) throws Exception {
    new Main().run();
}
 
//output methods
private void pn(Object o) {
    out.println(o);
}
private void p(Object o) {
    out.print(o);
}
private ArrayList < ArrayList < Integer >> ng(int n, int e) {
    ArrayList < ArrayList < Integer >> g = new ArrayList < > ();
    for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());
 
    for (int i = 0; i < e; ++i) {
        int u = ni(), v = ni();
        g.get(u).add(v);
        g.get(v).add(u);
    }
 
    return g;
}
 
private ArrayList < ArrayList < pair >> nwg(int n, int e) {
    ArrayList < ArrayList < pair >> g = new ArrayList < > ();
    for (int i = 0; i <= n; ++i) g.add(new ArrayList < > ());
 
    for (int i = 0; i < e; ++i) {
        int u = ni(), v = ni(), w = ni();
        
        g.get(u).add(new pair(w, v));
        g.get(v).add(new pair(w, u));
    }
 
    return g;
}
 
 
//input methods
private byte[] inbuf = new byte[1024];
public int lenbuf = 0, ptrbuf = 0;
 
 
private int readByte() {
    if (lenbuf == -1) throw new InputMismatchException();
    if (ptrbuf >= lenbuf) {
        ptrbuf = 0;
        try {
            lenbuf = is.read(inbuf);
        } catch (IOException e) {
            throw new InputMismatchException();
        }
        if (lenbuf <= 0) return -1;
    }
    return inbuf[ptrbuf++];
}
 
 
 
 
private boolean isSpaceChar(int c) {
    return !(c >= 33 && c <= 126);
}
private int skip() {
    int b;
    while ((b = readByte()) != -1 && isSpaceChar(b));
    return b;
}
 
private double nd() {
    return Double.parseDouble(ns());
}
private char nc() {
    return (char) skip();
}
 
private String ns() {
    int b = skip();
    StringBuilder sb = new StringBuilder();
    while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
        sb.appendCodePoint(b);
        b = readByte();
    }
    return sb.toString();
}
 
private char[] ns(int n) {
    char[] buf = new char[n];
    int b = skip(), p = 0;
    while (p < n && !(isSpaceChar(b))) {
        buf[p++] = (char) b;
        b = readByte();
    }
    return n == p ? buf : Arrays.copyOf(buf, p);
}
 
private char[][] nm(int n, int m) {
    char[][] map = new char[n][];
    for (int i = 0; i < n; i++) map[i] = ns(m);
    return map;
}
 
private int[] na(int n) {
    int[] a = new int[n];
    for (int i = 0; i < n; i++) a[i] = ni();
    return a;
}
 
private int ni() {
    int num = 0, b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private long nl() {
    long num = 0;
    int b;
    boolean minus = false;
    while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
    if (b == '-') {
        minus = true;
        b = readByte();
    }
 
    while (true) {
        if (b >= '0' && b <= '9') {
            num = num * 10 + (b - '0');
        } else {
            return minus ? -num : num;
        }
        b = readByte();
    }
}
 
private void tr(Object...o) {
    if (INPUT.length() > 0) System.out.println(Arrays.deepToString(o));
}
void watch(Object...a) throws Exception {
    int i = 1;
    print("watch starts :");
    for (Object o: a) {
        //print(o);
        boolean notfound = true;
        if (o.getClass().isArray()) {
 
            String type = o.getClass().getName().toString();
            //print("type is "+type);
            switch (type) {
                case "[I":
                    {
                        int[] test = (int[]) o;
                        print(i + " " + Arrays.toString(test));
                        break;
                    }
                case "[[I":
                    {
                        int[][] obj = (int[][]) o;
 
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[J":
                    {
 
                        long[] obj = (long[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[J":
                    {
 
                        long[][] obj = (long[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[D":
                    {
 
                        double[] obj = (double[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[D":
                    {
 
                        double[][] obj = (double[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[Ljava.lang.String":
                    {
 
                        String[] obj = (String[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[Ljava.lang.String":
                    {
 
                        String[][] obj = (String[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
                case "[C":
                    {
                        char[] obj = (char[]) o;
                        print(i + " " + Arrays.toString(obj));
                        break;
                    }
                case "[[C":
                    {
 
                        char[][] obj = (char[][]) o;
                        print(i + " " + Arrays.deepToString(obj));
                        break;
                    }
 
 
 
                default:
                    {
                        print(i + " type not identified");
                        break;
                    }
            }
            notfound = false;
 
        }
        if (o.getClass() == ArrayList.class) {
            print(i + " al: " + o);
            notfound = false;
        }
        if (o.getClass() == HashSet.class) {
            print(i + " hs: " + o);
            notfound = false;
        }
        if (o.getClass() == TreeSet.class) {
            print(i + " ts: " + o);
            notfound = false;
        }
        if (o.getClass() == TreeMap.class) {
            print(i + " tm: " + o);
            notfound = false;
        }
        if (o.getClass() == HashMap.class) {
            print(i + " hm: " + o);
            notfound = false;
        }
        if (o.getClass() == LinkedList.class) {
            print(i + " ll: " + o);
            notfound = false;
        }
        if (o.getClass() == PriorityQueue.class) {
            print(i + " pq : " + o);
            notfound = false;
        }
        if (o.getClass() == pair.class) {
            print(i + " pq : " + o);
            notfound = false;
        }
 
        if (notfound) {
            print(i + " unknown: " + o);
        }
        i++;
    }
    print("watch ends ");
}
 
}