/*
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 * To change this template file, choose Tools | Templates
 * and open the template in the editor.
 */
package internewt;

/**
 *
 * @author Student
 */
public class InterNewt {


    public static void main(String[] args) {
        double tabx[]={0,2,3,4,6};
        double taby[]={1,3,2,5,7};
        int x=1,f=0,g=1;
        double w=0;
        int q=tabx.length;
        int qq=q;
        double tabt[]= new double[q-1];
        double tabfx[]= new double[q];
        double tabwx[]= new double[q-1];
        tabfx[0]=taby[0];
        for (int k=0;k<q-1;k++){
            tabt[k]=(taby[k+1]-taby[k])/(tabx[k+1]-tabx[k]);
            if(g==1){
                tabfx[g]=tabt[k];
                g++;
            }
        }


        for (int i=0;i<qq;i++){
            for (int j=0; j<qq-2;j++){
             tabt[j]=(tabt[j+1]-tabt[j+0])/(tabx[j+f+2]-tabx[0+j]);
               if(j==0){
                   tabfx[g]=tabt[j];
                   g++;
               }
            }
            f+=1;
            qq-=1;
        }

        for (int i=0;i<q-1;i++){
            if(i==0)
            tabwx[i]=x-tabx[i];
            else if(i>0)
            tabwx[i]=tabwx[i-1]*(x-tabx[i]);
            }

        for (int i=0;i<q;i++){
            if (i==0)
                w+=taby[0];
            else
                w+=tabfx[i]*tabwx[i-1];

        }


        System.out.println(w);

    }





}