#include<iostream>
#include<iomanip>
#include<cmath>

using namespace std;
int main()
{
    cout.precision(6);
    cout.setf(ios::fixed);
    int n,i,j,k,flag=0,count=0;
    cout<<"\nEnter the no. of equations: ";           
    cin>>n;                    
    double a[n][n+1];            
    double x[n];                
    double eps,y;
    cout<<"\nEnter the elements of the augmented matrix (row is per equation without its variables and signs):\n";
    for (i=0;i<n;i++)
        for (j=0;j<=n;j++)
            cin>>a[i][j];

    cout<<"\nEnter the criteria for termination: ";
    cin>>eps;
    for (i=0;i<n;i++)                    
        for (k=i+1;k<n;k++)
            if (abs(a[i][i])<abs(a[i][k]))
                for (j=0;j<=n;j++)
                {
                    double temp=a[i][j];
                    a[i][j]=a[j][k];
                    a[k][j]=temp;
                }
    cout<<"\n(k)"<<setw(10);
    for(i=0;i<n;i++)
        cout<<"x"<<i<<setw(18);
    for (i=0;i<n;i++)
        cout<<"ek"<<i<<setw(18);
    cout<<"\n----------------------------------------------------------------------------------------------------------------";
    do                            
    {
        cout<<"\n"<<count+1<<setw(18);
        for (i=0;i<n;i++)                
        {
            y=x[i];
            x[i]=a[i][n];
            for (j=0;j<n;j++)
            {
                if (j!=i)
                x[i]=x[i]-a[i][j]*x[j];
            }
            x[i]=x[i]/a[i][i];
            if (abs(x[i]-y)<=eps)            
                flag++;
            cout<<x[i]<<setw(18);
      		 cout<<abs(x[i]-y)<<setw(18);
		}
        cout<<"\n";
        count++;   
    }while(flag<n);                        
    
    cout<<"\nThe solution is as follows:\n";
    for (i=0;i<n;i++)
        cout<<"x"<<i<<" = "<<x[i]<<endl;        
    return 0;
}