import java.io.*; import java.util.*; class Main { static long cube(long x){return x*x*x;} Main(){} long[] solveNaive(long[]a,long[]x,long[]y){ int n=a.length; long[]dp=new long[n+1]; Arrays.fill(dp,Long.MAX_VALUE); dp[0]=0; for(int i=0;i<n;++i){ for(int j=0;j<=i;++j){ dp[i+1]=Math.min(dp[i+1], dp[j]+cube(Math.abs(a[i]-x[j]))+cube(y[j])); } } return dp; } /* * i < j */ int calculateReversePoint(long[]a,long[]x,long[]y,int i,int j,long[]dp){ int n=a.length; int pass=n,fail=j-1; while(pass-fail>1){ int middle=(pass+fail)/2; long value1=dp[i]+cube(Math.abs(a[middle]-x[i]))+cube(y[i]); long value2=dp[j]+cube(Math.abs(a[middle]-x[j]))+cube(y[j]); if(value1>=value2)pass=middle; else fail=middle; } return pass; } long[] solveMongeDP(long[]a,long[]x,long[]y){ int n=a.length; long[]dp=new long[n+1]; Arrays.fill(dp,Long.MAX_VALUE); dp[0]=0; int[]deq=new int[n+1]; int[]rev=new int[n+1]; int s=0,t=0; for(int i=0;i<n;++i){ if(false){ System.err.println("deq:"); for(int j=s;j<t;++j){ System.err.print("("+deq[j]+","+rev[j]+") "); } System.err.println(); } int pre=i; long value=dp[pre]+cube(Math.abs(a[i]-x[pre]))+cube(y[pre]); //System.err.println("C("+pre+","+(i+1)+")="+value); // TODO imperfect while(s<t){ int oldPre=deq[t-1]; int revPoint=calculateReversePoint(a,x,y,oldPre,i,dp); long oldValue=dp[oldPre]+cube(Math.abs(a[i]-x[oldPre])) +cube(y[oldPre]); //System.err.println("C("+oldPre+","+(i+1)+")="+oldValue); if(revPoint<=i)t--; else if(t>=s+2&&rev[t-2]>=revPoint)t--; else{ rev[t-1]=revPoint; break; } } while(s<t){ if(rev[s]<=i)s++; else break; } deq[t]=i; t++; pre=deq[s]; value=dp[pre]+cube(Math.abs(a[i]-x[pre]))+cube(y[pre]); dp[i+1]=value; } return dp; } public static void main(String[] args) { MyScanner sc = new MyScanner(); out = new PrintWriter(new BufferedOutputStream(System.out)); int n=sc.nextInt(); long[]a=sc.nextLongArray(n); long[]x=sc.nextLongArray(n); long[]y=sc.nextLongArray(n); Main solver=new Main(); //long[]dp=solver.solveNaive(a,x,y); long[]dpMonge=solver.solveMongeDP(a,x,y); //System.err.println(Arrays.toString(dp)); //System.err.println(Arrays.toString(dpMonge)); out.println(dpMonge[n]); out.close(); } // http://codeforces.com/blog/entry/7018 //-----------PrintWriter for faster output--------------------------------- public static PrintWriter out; //-----------MyScanner class for faster input---------- public static class MyScanner { BufferedReader br; StringTokenizer st; public MyScanner() { br = new BufferedReader(new InputStreamReader(System.in)); } String next() { while (st == null || !st.hasMoreElements()) { try { st = new StringTokenizer(br.readLine()); } catch (IOException e) { e.printStackTrace(); } } return st.nextToken(); } int nextInt() { return Integer.parseInt(next()); } long nextLong() { return Long.parseLong(next()); } double nextDouble() { return Double.parseDouble(next()); } String nextLine(){ String str = ""; try { str = br.readLine(); } catch (IOException e) { e.printStackTrace(); } return str; } long[] nextLongArray(int n){ long[]r=new long[n]; for(int i=0;i<n;++i)r[i]=nextLong(); return r; } } }