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.math.BigInteger;
		import java.util.*;
			
			
			public class Practice {
				private static InputStream stream;
				private static byte[] buf = new byte[1024];
				private static int curChar;
				private static int numChars;
				private static SpaceCharFilter filter;
				private static PrintWriter pw;
				private static long mod=1000000007;
			
			    public static void main(String[] args) {
			    	InputReader(System.in);
					pw = new PrintWriter(System.out); 
			        new Thread(null ,new Runnable(){
			           public void run(){
			               try{
			                   solve();//This is solution method
		               pw.close();
		           } catch(Exception e){
		               e.printStackTrace();
		           }
		       }
		   },"1",1<<26).start();
			    				   }
			    public static void Merge(long a[],int p,int r){
		            if(p<r){
		                int q = (p+r)/2;
		                Merge(a,p,q);
		                Merge(a,q+1,r);
		                Merge_Array(a,p,q,r);
		            }
		        }
		        public static void Merge_Array(long a[],int p,int q,int r){
		           long b[] = new long[q-p+1];
		            long c[] = new long[r-q];
		            for(int i=0;i<b.length;i++)
		                b[i] = a[p+i];
		            for(int i=0;i<c.length;i++)
		                c[i] = a[q+i+1];
		            int i = 0,j = 0;
		            for(int k=p;k<=r;k++){
		                if(i==b.length){
		                    a[k] = c[j];
		                    j++;
		                }
		                else if(j==c.length){
		                    a[k] = b[i];
		                    i++;
		                }
		                else if(b[i]<c[j]){
		                    a[k] = b[i];
		                    i++;
		                }
		                else{
		                    a[k] = c[j];
		                    j++;
		                }
		            }
		        }    
			    				    
	    					public static void solve() {
	        		    	
	    						int n=nextInt();
	    						double a[][]=new double[n][n]; 
	        		    	
	    						for(int i=0;i<n;i++){
	    							String token[]=nextLine().split(" ");
	    							for(int j=0;j<n;j++){
	    								a[i][j]=Double.parseDouble(token[j]);
	    							}
	    						}
	    						double dp[]=new double[(1<<n)+1];
	    						dp[(1<<n)-1]=1;
	    						for(int mask=(1<<n)-1;mask>0;mask--){
	    							int cnt=Integer.bitCount(mask);
	    							for(int j=0;j<n;j++){
	    								
	    								if((mask &(1<<j))>0){
	    									
	    									for(int k=j+1;k<n;k++){
	    										if((mask & (1<<k))>0){
	    											dp[mask ^ (1<<j)]+=a[k][j] * dp[mask]/ (cnt* (cnt-1)/2); 	
	    											dp[mask ^ (1<<k)]+=a[j][k] * dp[mask]/ (cnt*(cnt-1)/2); 		
	    											
	    										}
	    									}
	    								}
	    							}
	    						}
	    						for(int i=0;i<n;i++){
	    							System.out.printf("%.6f ",dp[1<<i]);
	    						}
	    					}
	        		    	
	        		        
	        		    	 	
		        		    		
		        		    				
		        		        
		public static boolean isVowel(char c){        		    		
			if(c=='a' || c=='i'|| c=='e' || c=='o' || c=='u')
					return true;
				return false;
			}
			
			
		    public static String reverseString(String s) {
				StringBuilder sb = new StringBuilder(s);
				sb.reverse();
				return (sb.toString());
			}
		    private static BigInteger ncr(int n,int k){
		    	if (k < 0 || k > n) return BigInteger.ZERO;
		        if (n-k < k) k = n-k;
		
		        BigInteger x = BigInteger.ONE;
		        for (int i = 1; i <= k; i++) {
		            x = x.multiply(new BigInteger(""+(n-i+1)));
		x = x.divide(new BigInteger(""+i));
		        }
		
		return x;
		    }
		    static long fact[];
		private static void factmod(int n,int mod){
			fact=new long[n+1];
			fact[0]=1;
			for(int i=1;i<=n;i++){
				fact[i]=i*fact[i-1];
				//fact[i]%=mod;
		
			}
			
		}
		private static long phi(long n){
			long ans=n;
			if(n%2==0)
				ans-=(ans/2);
			while(n%2==0)
			{
				n/=2;
				
			}
			for(int i=3;i*i<=n;i+=2){
				if(n%i==0){
				while(n%i==0){
					n/=i;
				}
				ans-=(ans/i);
				}
			}
			if(n>2)
				ans-=(ans/n);
			
			return ans;
		}
		static long d,x,y;
		static long modInverse(long A, long M)
		{
		extendedEuclid(A,M);
		return (x%M+M)%M;    //x may be negative
		}
		static void extendedEuclid(long A, long B) {
		if(B == 0) {
		d = A;
		x = 1;
		y = 0;
		}
		else {
		extendedEuclid(B, A%B);
		long temp = x;
		x = y;
		y = temp - (A/B)*y;
		}
		}
		static boolean prime[];
		static int spf[];
		public static void sieve(int n){
			prime=new boolean[n+1];
			spf=new int[n+1];
			
			Arrays.fill(spf, 1);
			Arrays.fill(prime, true);
		prime[1]=false;
			spf[2]=2;
			for(int i=4;i<=n;i+=2)
			{
				spf[i]=2;
				prime[i]=false;
			}
		
		for(int i=3;i<=n;i+=2){
			if(prime[i]){
				spf[i]=i;
				for(int j=2*i;j<=n;j+=i){
					
					prime[j]=false;
				if(spf[j]==1){
					spf[j]=i;
				}
				}
			}
		}
			
		}
		public static boolean isPrime(long n) {
			
			if (n <= 1)
				return false;
			if (n <= 3)
				return true;
		
			if (n % 2 == 0 || n % 3 == 0)
				return false;
		
			for (long i = 5; i * i <= n; i = i + 6)
				if (n % i == 0 || n % (i + 2) == 0)
					return false;
		
			return true;
		}
		
		    
			public static long gcd(long x, long y) {
				if (x == 0)
					return y;
				else
					return gcd( y % x,x);
			}
			
			
			public static void InputReader(InputStream stream1) {
				stream = stream1;
			}
		 
			private static boolean isWhitespace(int c) {
				return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
			}
		 
			private static boolean isEndOfLine(int c) {
				return c == '\n' || c == '\r' || c == -1;
			}
		 
			private static 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++];
			}
		 
			private static 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 - '0';
					c = read();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
		 
			private static long nextLong() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				int sgn = 1;
				if (c == '-') {
			sgn = -1;
			c = read();
		}
		long res = 0;
		do {
			if (c < '0' || c > '9')
			throw new InputMismatchException();
		res *= 10;
		res += c - '0';
					c = read();
				} while (!isSpaceChar(c));
				return res * sgn;
			}
		 
			private static String nextToken() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isSpaceChar(c));
				return res.toString();
			}
			private static double nextDouble() {
				return Double.parseDouble(nextLine());
			}
			private static String nextLine() {
				int c = read();
				while (isSpaceChar(c))
					c = read();
				StringBuilder res = new StringBuilder();
				do {
					res.appendCodePoint(c);
					c = read();
				} while (!isEndOfLine(c));
				return res.toString();
			}
		 
			private static int[] nextIntArray(int n) {
				int[] arr = new int[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextInt();
				}
				return arr;
			}
		 
			private static int[][] next2dArray(int n, int m) {
				int[][] arr = new int[n][m];
				for (int i = 0; i < n; i++) {
					for (int j = 0; j < m; j++) {
						arr[i][j] = nextInt();
					}
				}
				return arr;
			}
			private static char[][] nextCharArray(int n,int m){
				char [][]c=new char[n][m];
				for(int i=0;i<n;i++){
					String s=nextLine();
					for(int j=0;j<s.length();j++){
						c[i][j]=s.charAt(j);
					}
				}
				return c;
			}
		 
			private static long[] nextLongArray(int n) {
				long[] arr = new long[n];
				for (int i = 0; i < n; i++) {
					arr[i] = nextLong();
				}
				return arr;
			}
		 
			private static void pArray(int[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static void pArray(long[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static void pArray(boolean[] arr) {
				for (int i = 0; i < arr.length; i++) {
					pw.print(arr[i] + " ");
				}
				pw.println();
				return;
			}
		 
			private static boolean isSpaceChar(int c) {
				if (filter != null)
					return filter.isSpaceChar(c);
				return isWhitespace(c);
			}
		 
			private interface SpaceCharFilter {
				public boolean isSpaceChar(int ch);
			}
		
			
		}	
			 class Hashing {
				 
				  static final int multiplier = 43;
				  static final Random rnd = new Random();
				  static final int mod1 = BigInteger.valueOf((int) (1e9 + rnd.nextInt((int) 1e9))).nextProbablePrime().intValue();
				  static final int mod2 = BigInteger.valueOf((int) (1e9 + rnd.nextInt((int) 1e9))).nextProbablePrime().intValue();
				  static final int invMultiplier1 = BigInteger.valueOf(multiplier).modInverse(BigInteger.valueOf(mod1)).intValue();
				  static final int invMultiplier2 = BigInteger.valueOf(multiplier).modInverse(BigInteger.valueOf(mod2)).intValue();
		 
				  long[] hash1, hash2;
				  long[] inv1, inv2;
				  int n;
		 
				  public Hashing(String s) {
				    n = s.length();
				    hash1 = new long[n + 1];
				    hash2 = new long[n + 1];
				    inv1 = new long[n + 1];
				    inv2 = new long[n + 1];
				    inv1[0] = 1;
				    inv2[0] = 1;
		 
				    long p1 = 1;
				    long p2 = 1;
				    for (int i = 0; i < n; i++) {
				      hash1[i + 1] = (hash1[i] + s.charAt(i) * p1) % mod1;
				      p1 = p1 * multiplier % mod1;
				      inv1[i + 1] = inv1[i] * invMultiplier1 % mod1;
				      hash2[i + 1] = (hash2[i] + s.charAt(i) * p2) % mod2;
				      p2 = p2 * multiplier % mod2;
				      inv2[i + 1] = inv2[i] * invMultiplier2 % mod2;
				    }
				  }
		 
				  public long getHash(int i, int r) {
					//  i--;
				    return (((hash1[r] - hash1[i] + mod1) * inv1[i] % mod1) << 32)
				        + (hash2[r] - hash2[i] + mod2) * inv2[i] % mod2;
				  }
			}
