*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 *a*<sub class="lower-index">*ij*</sub>, and the second will eat up the first with the probability *a*<sub class="lower-index">*ji*</sub> = 1 - *a*<sub class="lower-index">*ij*</sub>. 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.
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*. *a*<sub class="lower-index">*ij*</sub> (0 ≤ *a*<sub class="lower-index">*ij*</sub> ≤ 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: *a*<sub class="lower-index">*ij*</sub> = 1 - *a*<sub class="lower-index">*ji*</sub>. All real numbers are given with not more than 6 characters after the decimal point.
2
0 0.5
0.5 0
0.500000 0.500000 
4
0 0.5 0.5 0.5
0.5 0 0.5 0.5
0.5 0.5 0 0.5
0.5 0.5 0.5 0
0.250000 0.250000 0.250000 0.250000 
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
1.000000 0.000000 0.000000 0.000000 0.000000 
1
0.000
1.000000 
2
0.000 0.551
0.449 0.000
0.551000 0.449000 
3
0.000 0.817 0.584
0.183 0.000 0.665
0.416 0.335 0.000
0.564400 0.208967 0.226632 
4
0.000 0.083 0.548 0.503
0.917 0.000 0.395 0.144
0.452 0.605 0.000 0.991
0.497 0.856 0.009 0.000
0.163512 0.222554 0.463543 0.150390 
5
0.000 0.349 0.202 0.088 0.431
0.651 0.000 0.435 0.627 0.564
0.798 0.565 0.000 0.725 0.949
0.912 0.373 0.275 0.000 0.027
0.569 0.436 0.051 0.973 0.000
0.059303 0.233839 0.494324 0.093917 0.118617 
8
0.000 0.147 0.783 0.224 0.220 0.651 0.453 0.209
0.853 0.000 0.246 0.076 0.018 0.349 0.896 0.315
0.217 0.754 0.000 0.307 0.968 0.400 0.531 0.086
0.776 0.924 0.693 0.000 0.707 0.842 0.116 0.949
0.780 0.982 0.032 0.293 0.000 0.908 0.307 0.266
0.349 0.651 0.600 0.158 0.092 0.000 0.066 0.909
0.547 0.104 0.469 0.884 0.693 0.934 0.000 0.251
0.791 0.685 0.914 0.051 0.734 0.091 0.749 0.000
0.056312 0.054963 0.091124 0.315966 0.093803 0.056812 0.187952 0.143068 
#pragma GCC target ("avx2")
#pragma GCC optimization ("O3")
#pragma GCC optimization ("unroll-loops")
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#include <iostream>
#include <stdio.h>
#include <iterator>
#include <vector>
#include <cstdlib>
#include <iostream> 
#include <queue>
#include <map>
#include <bits/stdc++.h>
using namespace std; 
typedef unsigned long long ll;
typedef long double lld;
typedef pair<int,int> pi;
#define FastIO cin.sync_with_stdio(false),cin.tie(NULL)
#define ll        long long 
#define mod       (ll) 1000000007
#define pb        push_back
#define f(i,s,n)    for (int i=s;i<n;i++)
#define fb(i,s,n,b)    for (int i=s;i<n;i+=b)
#define frev(i,s,n) for(int i=s;i>n;i--)
#define vii       vector<int>
#define seti      set<int>
#define pairi      pair<int,int>
#define mapi      unordered_map<int,int>
#define mapv      map<int,vii>
#define vll       vector<ll>
#define vpp       vector<pp>
#define vss       vector<string>
#define lcm(a,b)    (a*b)/__gcd(a,b)
#define all(a)      a.begin(),a.end()
#define all(a)      a.begin(),a.end()
#define fo(i,a)       for(auto &i:a)
#define bs(v,x)     binary_search(all(v),x)
#define fast ios_base::sync_with_stdio(false),cin.tie(nullptr),cout.tie(nullptr);srand(time(NULL))
#define sortrev(a) sort(a.begin(), a.end(), greater<pair<pair<int,int>,int>>());
#define vii2d       vector<vector<int>>
#define ms          multiset<int>
#define pairi       pair<int,int>
#define useti   unordered_set<int>
#define mp          make_pair
#define gcd(a,b)    __gcd(a,b)
#define ff first 
#define se second
using namespace __gnu_pbds;
typedef tree<ll, null_type, less<ll>, rb_tree_tag, tree_order_statistics_node_update > pbds;
vector<double> dp(524288,-1.0); 
int n;
double a[18][18];
double find(int mask)
{
    if (dp[mask]!=-1)
        return dp[mask];
    if (mask==0)
    {
        dp[mask]=1,0;
        return 1.0;
    }
    dp[mask]=0;
    vii dead;
    vii alive;
    f(i,0,n)
    {
        int bitmask=(1<<i);
        int bit=mask&bitmask;
        if (bit>0)
        {
            dead.pb(i);
        }
        else
        {
            alive.pb(i);
        }
    }
    int si=alive.size()+1;
    double prob=2/((double)si*(si-1));
    f(i,0,dead.size())
    {
        f(j,0,alive.size())
        {
            dp[mask]+=find(mask^(1<<dead[i]))*prob*a[alive[j]][dead[i]];
        }
    }
    return dp[mask];
}

void solve(int ik)
{
    vector<double> ans;
    cin>>n;
    f(i,0,n)
    {
        f(j,0,n)
        {
            cin>>a[i][j];
        }
    }
    int all=(1<<n)-1;
    f(i,0,n)
    {
        double ans=find(all^(1<<i));
        cout<<ans<<" ";
    }
    cout<<endl;
}
int main()
{
   fast;
   #ifndef ONLINE_JUDGE
   freopen("input.txt","r",stdin);
   freopen("output.txt","w",stdout);
   #endif
    int t=1;
    int c=0;
    while(t--)
    {
      solve(c);
      c+=1;
    }
    return 0; 
}