package main

import (
    "fmt"
    "github.com/skorobogatov/input"
    "math/big"
)

func main() {
        n:= 0
        fmt.Scanf("%d",&n)
	a:=make([][]*big.Rat,0)
	b:=make([]*big.Rat,n,n)
	for i := 0; i < n; i++ {
		mas := make([]*big.Rat, n, n)
		a = append(a, mas)
	}
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			var q int64
			input.Scanf("%d", &q)
			a[i][j] = big.NewRat(q,1)
		}
		var q int64
		input.Scanf("%d", &q)
		b[i] = big.NewRat(q,1)
	}
	fmt.Printf("vvod:\n%v\n%v\n",a,b)
	//diagonalizewoutnul
	for i:=0;i<n;i++ {
		if a[i][i].Sign()==0 {
			for j:=i+1;j<n;j++ {
				if i!=j {
					if a[j][i].Sign()!=0 /*&& a[i][j]!=0 */{
						for k:=0;k<n;k++ {
							temp:=a[j][k]
							a[j][k]=a[i][k]
							a[i][k]=temp
						}
						temp:=b[j]
						b[j]=b[i]
						b[i]=temp
						break
					}
				}
			}
		}
	}
	fmt.Printf("bez nul na diag:\n%v\n%v\n",a,b)
	//gauss
	
	for k:=0;k<n;k++ {
		for i:=k+1;i<n;i++ {
			if a[k][k].Sign()==0 {
				fmt.Printf("nosol")
				return
			}
			m:=big.NewRat(1,1)
			m=m.Quo(a[i][k],a[k][k])
			for j:=k;j<n;j++ {
				f:=big.NewRat(1,1)
				a[i][j]=a[i][j].Sub(a[i][j],f.Mul(m,a[k][j]))
			}
			f:=big.NewRat(1,1)
			b[i]=b[i].Sub(b[i],f.Mul(m,b[k]))
		}
	}
	fmt.Printf("gauss:\n%v\n%v\n",a,b)
	
	x:=make([]*big.Rat,n,n)
	for i:=0;i<n;i++ {
		x[i]=big.NewRat(0,1)
	}
	for i:=n-1;i>=0;i-- {
		var s *big.Rat
		s=big.NewRat(0,1)
		for j:=i;j<n;j++ {
			f:=big.NewRat(0,1)
			s=s.Add(s,f.Mul(a[i][j],x[j]))
		}
		f:=big.NewRat(0,1)
		//g:=big.NewRat(0,1)
		//g=s
		fmt.Printf("%v\n,%v\n",f.Sub(b[i],s.Neg(s)),a[i][i])
		x[i]=x[i].Quo(f.Sub(b[i],s.Neg(s)),a[i][i])
		fmt.Printf("%v\n,%v\n",a,b)
	}
	fmt.Printf("solutions:\n%v\n",x)
}