You are given two arrays A and B, each of size n. The error, E, between these two arrays is defined <image>. You have to perform exactly k1 operations on array A and exactly k2 operations on array B. In one operation, you have to choose one element of the array and increase or decrease it by 1.

Output the minimum possible value of error after k1 operations on array A and k2 operations on array B have been performed.

Input

The first line contains three space-separated integers n (1 ≤ n ≤ 103), k1 and k2 (0 ≤ k1 + k2 ≤ 103, k1 and k2 are non-negative) — size of arrays and number of operations to perform on A and B respectively.

Second line contains n space separated integers a1, a2, ..., an ( - 106 ≤ ai ≤ 106) — array A.

Third line contains n space separated integers b1, b2, ..., bn ( - 106 ≤ bi ≤ 106)— array B.

Output

Output a single integer — the minimum possible value of <image> after doing exactly k1 operations on array A and exactly k2 operations on array B.

Examples

Input

2 0 0
1 2
2 3


Output

2

Input

2 1 0
1 2
2 2


Output

0

Input

2 5 7
3 4
14 4


Output

1

Note

In the first sample case, we cannot perform any operations on A or B. Therefore the minimum possible error E = (1 - 2)2 + (2 - 3)2 = 2. 

In the second sample case, we are required to perform exactly one operation on A. In order to minimize error, we increment the first element of A by 1. Now, A = [2, 2]. The error is now E = (2 - 2)2 + (2 - 2)2 = 0. This is the minimum possible error obtainable.

In the third sample case, we can increase the first element of A to 8, using the all of the 5 moves available to us. Also, the first element of B can be reduced to 8 using the 6 of the 7 available moves. Now A = [8, 4] and B = [8, 4]. The error is now E = (8 - 8)2 + (4 - 4)2 = 0, but we are still left with 1 move for array B. Increasing the second element of B to 5 using the left move, we get B = [8, 5] and E = (8 - 8)2 + (4 - 5)2 = 1.
import java.awt.Checkbox;
import java.awt.Point;
import java.io.*;
                    import java.math.*;
                    import java.util.*;
import java.util.Map.Entry;

import javax.print.attribute.SetOfIntegerSyntax;
import javax.swing.plaf.FontUIResource;




             
                    public class CODE2{
                      private static InputStream stream;
                        private static byte[] buf = new byte[1024];
                        private static int curChar,MAX;
                        private static int numChars;
                        private static SpaceCharFilter filter;
                        private static PrintWriter pw;
                        private static long count = 0,mod=1000000007;
                        static int BIT[];
                        private static boolean primer[];
                    //    private static TreeSet<Integer> ts=new TreeSet[200000];
public final static int INF = (int) 1E9;

public static void main(String args[]) {
    InputReader(System.in);
    pw = new PrintWriter(System.out); 
    new Thread(null ,new Runnable(){
       public void run(){
           try{
               solve();
               
               pw.close();
           } catch(Exception e){
               e.printStackTrace();
           }
       }
   },"1",1<<26).start();
   }
    static StringBuilder sb;
    public static void test(){
         sb=new StringBuilder();
        int t=nextInt();
        while(t-->0){
            
            solve();
           
        }
        pw.println(sb);
    }
    public static long pow(long n, long p,long mod) {
        if(p==0)
            return 1;
        if(p==1)
            return n%mod;
        if(p%2==0){
            long temp=pow(n, p/2,mod);
        return (temp*temp)%mod;
        }else{
                 long temp=pow(n,p/2,mod);
                 temp=(temp*temp)%mod;
                 return(temp*n)%mod;
                 
        }
    }
    public static long pow(long n, long p) {
        if(p==0)
            return 1;
        if(p==1)
            return n;
        if(p%2==0){
            long temp=pow(n, p/2);
        return (temp*temp);
        }else{
                 long temp=pow(n,p/2);
                 temp=(temp*temp);
                 return(temp*n);
                 
        }
    }
    public static void Merge(long a[],int p,int r){
        if(p<r){
            int q = (p+r)/2;
            Merge(a,p,q);
            Merge(a,q+1,r);
            Merge_Array(a,p,q,r);
        }
    }
    public static void Merge_Array(long a[],int p,int q,int r){
       long b[] = new long[q-p+1];
        long c[] = new long[r-q];
        for(int i=0;i<b.length;i++)
            b[i] = a[p+i];
        for(int i=0;i<c.length;i++)
            c[i] = a[q+i+1];
        int i = 0,j = 0;
        for(int k=p;k<=r;k++){
            if(i==b.length){
                a[k] = c[j];
                j++;
            }
            else if(j==c.length){
                a[k] = b[i];
                i++;
            }
            else if(b[i]<c[j]){
                a[k] = b[i];
                i++;
            }
            else{
                a[k] = c[j];
                j++;
            }
        }
    }
    
  
    public static long gcd(long x, long y) {
        if (x == 0)
            return y;
        else
            return gcd( y % x,x);
    }    
    
    public static boolean isPrime(int n) {
        if (n <= 1)
            return false;
        if (n <= 3)
            return true;
 
        if (n % 2 == 0 || n % 3 == 0)
            return false;
 
        for (int i = 5; i * i <= n; i = i + 6)
            if (n % i == 0 || n % (i + 2) == 0)
                return false;
        return true;
    }
    
     //   static LinkedList<Integer> adj[];
        static ArrayList<Integer> adj[];
        static boolean Visited[];
        static HashSet<Integer> exc;
        static long oddsum[]=new long[1000001];
        static long co=0,ans=0;
        static int parent[];
        static int size[],color[],res[],k;
        static ArrayList<Integer> al[];
        static long MOD = (long)1e9 + 7;
    /*    private static void buildgraph(int n){
            adj=new LinkedList[n+1];
            Visited=new boolean[n+1];
            levl=new int[n+1];
            
            for(int i=0;i<=n;i++){
                adj[i]=new LinkedList<Integer>();
            
            }


        }
*/      
       
        static int[] levl,dist;
        static int[] eat;
      //  static int n,m;
      //  static int n;
   //     static int price[];
        //ind frog crab
   static  boolean check(char c)
    {
    	if(c!='a' && c!='e' && c!='i' && c!='o' && c!='u' )
    		return true;
    	else
    		return false;
    }
   static int nm = 1000007;
   static boolean divisor[];
   static void sprime()
   {
	   spf=new int[nm+1];
	   for(int i=2;i<nm;i++)
	   {
		   if(spf[i]!=0)
			   continue;
		   for(int j=i;j<nm;j+=i)
		   {
			   spf[j] = i;
		   }
	   }
   }
        public static void solve(){
      
        	int n = nextInt();
        	int k1 = nextInt();
        	int k2 = nextInt();
        	
        	int a[] = new int[n];
        	int b[] = new int[n];
        	
        	a = nextIntArray(n);
        	b = nextIntArray(n);
        	
        	Comparator comp = new pa();
        	PriorityQueue<Integer> pq = new PriorityQueue<>(comp);
        	
        	int total = k1+k2;
        	
        	
        	for(int i=0;i<n;i++)
        	{
        		pq.add(Math.abs(a[i]-b[i]));
        	}
        
        	while(total>0)
        	{
        		int x = pq.poll();
        		
        		if(x>0)
        		{
        			x--;
        			pq.add(x);
        		}
        		else if(x<0)
        		{
        			x++;
        			pq.add(x);
        		}
        		else
        		{
        			if(total%2==1)
        			{
        				pq.add(1);
        			}
        			else
        				pq.add(0);
        			
        			break;
        		}
        		
        		total--;
        	}
        	
        	long ans = 0;
        	while(!pq.isEmpty())
        	{
        		int x = pq.poll();
        		
        		ans+=(long)x * (long)x;
        	}
        	System.out.println(ans);
        	
        	
        	
      }
      
      
        static class pa implements Comparator<Integer>
    	{
    		

    		
    		public int compare(Integer a,Integer b)
    		{
    			return b-a;
    					
    		}
    	}
        static class node implements Comparable<node>
    	{
    		int u;long w;
    		
    		node(int u,long w)
    		{
    			this.u = u;
    			this.w = w; 
    		}
    		
    		public int compareTo(node other)
    		{
    			return (int)(this.w-other.w);
    					
    		}
    	}
        static long calculate(long p)
        {
        	long mod2 = 500000004;
        	p=((p%MOD)*(p+1)%MOD)%MOD;
        	p = (p * (mod2)%MOD)%MOD;
        	return p;
        }
        static String decrypt(int x)
        {
        	if(x<4)
        		return "NO";
        	ArrayList<Integer> factors = new ArrayList<>();
        	int backup = x;
        	while(x!=1)
        	{
        		int sp = spf[x];
        		factors.add(sp);
        		while(x%sp ==0)
        		x = x / sp;
        		
        	}
        	for(int i=0;i<factors.size();i++)
        	{
        		for(int j=0;j<factors.size();j++)
        		{
        			
        			if(backup % (factors.get(i)*factors.get(j)) == 0 )
        			{
        				int tt = backup / (factors.get(i)*factors.get(j));
        				
        				if(tt==1 || divisor[tt])
        					return "YES";
        					
        			}
        		}
        	}
        	return "NO";
        }
        
       static  long maxSubArraySum(int a[], int size)
        {
           long max_so_far = a[0];
           long curr_max = a[0];
         
           for (int i = 1; i < size; i++)
           {
                curr_max = Math.max(a[i], curr_max+a[i]);
                max_so_far = Math.max(max_so_far, curr_max);
           }
           return max_so_far;
        }
        
        static void seive2(int n)
        {
        	primer=new boolean[n+1];
        	Arrays.fill(primer,true);
        	primer[0]=false;
        	primer[1]=false;
        	primer[2]=true;
        	
        	for(int i=2;i*i<=n;i++)
        	{
        		if(primer[i])
        		{
        			for(int j=2*i;j<=n;j=j+i)
        			{
        				primer[j]=false;
        			}
        		}
        	}
        }
       
        
     /*   static void BITupdate(int x,int val)
        {
        	while(x<=n)
        	{
        		BIT[x]+=val;
        		x+= x & -x;
        	}
        }*/
     /*   static void update(int x,long val)
        {
      
        	val=val%MOD;
        	while(x<=n)
        	{
        		// System.out.println(x);
        	BIT[x]=(BIT[x]+val)%MOD;
        	x+=(x & -x);
        	}
        //	System.out.println("dfd");
        }*/
        static int BITsum(int x)
        		{
        	int sum=0;
        	while(x>0)
        	{
        		sum+=BIT[x];
        		x-= (x & -x);
        	}
        		return sum;
        		}
  /*      static long sum(int x)
        {
        	long sum=0;
        	while(x>0)
        	{
        		sum=(sum+BIT[x])%MOD;
        		x-=x & -x;
        	}
        	return sum;
        }*/
        static boolean union(int x,int y)
        {
        	int xr=find(x);
        	int yr=find(y);
        	if(xr==yr)
        		return false;
        	if(size[xr]<size[yr])
        	{
        		size[yr]+=size[xr];
        		parent[xr]=yr;
        	}
        	else
        	{
        		size[xr]+=size[yr];
        		parent[yr]=xr;
        		
        	}
        	return true;
        	
        }
        static int  find(int x)
        {
        	if(parent[x]==x)
        		return x;
        	else
        	{
        		parent[x]=find(parent[x]);
        		return parent[x];
        	}
        	
        }
        public static class Edge implements Comparable<Edge>
        {
        	int u, v;
			public Edge(int u, int v) 
			{
				this.u = u;
				this.v = v;
				//this.s = s;
			}
			public int hashCode() 
			{
				return Objects.hash();
			}
			public int compareTo(Edge other) 
			{
			return (Integer.compare(u, other.u) != 0 ? (Integer.compare(u, other.u)):(Integer.compare(v, other.v)));
				//		&((Long.compare(s, other.s) != 0 ? (Long.compare(s, other.s)):(Long.compare(u, other.v)!=0?Long.compare(u, other.v):Long.compare(v, other.u))));
				//return this.u-other.u;
			}
			public String toString()
			{
				return this.u + " " + this.v;
			}
        }
       
        static int col[];
    public static boolean isVowel(char c){
        if(c=='a' || c=='e'||c=='i' || c=='o' || c=='u')
            return true;
        return false;
    }
static int no_vert=0;

  /*private static void dfs(int start){
      Visited[start]=true;
    if(al[color[start]].size()>=k)
    {
    	res[start]=al[color[start]].get(al[color[start]].size()-k);
    }
    al[color[start]].add(start);
      for(int i:adj[start]){
          if(!Visited[i])
              {
              dfs(i);
              }
      }
      (al[color[start]]).remove(al[color[start]].size()-1);
      
  }
    */
    public static String reverseString(String s) {
        StringBuilder sb = new StringBuilder(s);
        sb.reverse();
        return (sb.toString());
    }
    
  /*  
   private static void BFS(int sou){
        Queue<Integer> q=new LinkedList<Integer>();
        q.add(sou);
        Visited[sou]=true;
        levl[sou]=0;
        while(!q.isEmpty()){
            int top=q.poll();
            
            for(int i:adj[top]){
                //pw.println(i+" "+top);
            if(!Visited[i])
            {
                
                q.add(i);
                levl[i]=levl[top]+1;
            }
            
            Visited[i]=true;
            
            }
        }
    }*/
    



                  static int indeg[];
               /* private static void kahn(int n){
                    
                    PriorityQueue<Integer> q=new PriorityQueue<Integer>();
                    for(int i=1;i<=n;i++){
                        if(indeg[i]==0){
                            q.add(i);
                        }
                    }
                    while(!q.isEmpty()){
                        int top=q.poll();
                        st.push(top);
                        for(Node i:adj[top]){
                            indeg[i.to]--;
                            if(indeg[i.to]==0){
                                q.add(i.to);
                            }
                        }
                    }
                }
                    
                    static int state=1;
                    static long no_exc=0,no_vert=0;
                  static Stack<Integer> st;
                  static HashSet<Integer> inset;
                 /*   private static void topo(int curr){
                        
                        Visited[curr]=true;
                        inset.add(curr);
                        for(int x:adj[curr]){
                            if(adj[x].contains(curr) || inset.contains(x)){
                                state=0;
                                return;
                            }
                            if(state==0)
                                return;
                            
                        }
                        st.push(curr);
                        
                        inset.remove(curr);
                    }*/
                    static HashSet<Integer> hs;
                   
                 
                     static boolean prime[];
                    static int spf[];
                    public static void sieve(int n){
                        prime=new boolean[n+1];
                        spf=new int[n+1];
                        
                        Arrays.fill(spf, 1);
                        Arrays.fill(prime, true);
                    prime[1]=false;
                        spf[2]=2;
                        
                    
                    for(int i=2;i*i<=n;i++){
                        if(prime[i]){
                            spf[i]=i;
                            for(int j=2*i;j<=n;j+=i){
                                
                                prime[j]=false;
                           
                            }
                        }
                    }
                    
                        
                    }
                     
                    // To Get Input
// Some Buffer Methods
 
                     public static void sort(long a[]){
                         Merge(a, 0, a.length-1);
                     }
                    public static void InputReader(InputStream stream1) {
                        stream = stream1;
                    }
 
                    private static boolean isWhitespace(int c) {
                        return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
                    }
 
                    private static boolean isEndOfLine(int c) {
                        return c == '\n' || c == '\r' || c == -1;
                    }
 
                    private static int read() {
                        if (numChars == -1)
                            throw new InputMismatchException();
                        if (curChar >= numChars) {
                            curChar = 0;
                            try {
                                numChars = stream.read(buf);
                            } catch (IOException e) {
                                throw new InputMismatchException();
                            }
                            if (numChars <= 0)
                                return -1;
                        }
                        return buf[curChar++];
                    }
 
                    private static int nextInt() {
                        int c = read();
                        while (isSpaceChar(c))
                            c = read();
                        int sgn = 1;
                        if (c == '-') {
        sgn = -1;
        c = read();
    }
    int res = 0;
    do {
        if (c < '0' || c > '9')
            throw new InputMismatchException();
        res *= 10;
        res += c - '0';
                            c = read();
                        } while (!isSpaceChar(c));
                        return res * sgn;
                    }
 
                    private static long nextLong() {
                        int c = read();
                        while (isSpaceChar(c))
                            c = read();
                        int sgn = 1;
                        if (c == '-') {
        sgn = -1;
        c = read();
    }
    long res = 0;
    do {
        if (c < '0' || c > '9')
            throw new InputMismatchException();
        res *= 10;
        res += c - '0';
                            c = read();
                        } while (!isSpaceChar(c));
                        return res * sgn;
                    }
 
                    private static String nextToken() {
                        int c = read();
                        while (isSpaceChar(c))
                            c = read();
                        StringBuilder res = new StringBuilder();
                        do {
                            res.appendCodePoint(c);
                            c = read();
                        } while (!isSpaceChar(c));
                        return res.toString();
                    }
 
                    private static String nextLine() {
                        int c = read();
                        while (isSpaceChar(c))
                            c = read();
                        StringBuilder res = new StringBuilder();
                        do {
                            res.appendCodePoint(c);
                            c = read();
                        } while (!isEndOfLine(c));
                        return res.toString();
                    }
 
                    private static int[] nextIntArray(int n) {
                        int[] arr = new int[n];
                        for (int i = 0; i < n; i++) {
                            arr[i] = nextInt();
                        }
                        return arr;
                    }
 
                    private static long[][] next2dArray(int n, int m) {
                        long[][] arr = new long[n][m];
                        for (int i = 0; i < n; i++) {
                            for (int j = 0; j < m; j++) {
                                arr[i][j] = nextLong();
                            }
                        }
                        return arr;
                    }
                    private static char[][] nextCharArray(int n,int m){
                        char [][]c=new char[n][m];
                        for(int i=0;i<n;i++){
                            String s=nextLine();
                            for(int j=0;j<s.length();j++){
                                c[i][j]=s.charAt(j);
                            }
                        }
                        return c;
                    }
 
                    private static long[] nextLongArray(int n) {
                        long[] arr = new long[n];
                        for (int i = 0; i < n; i++) {
                            arr[i] = nextLong();
                        }
                        return arr;
                    }
 
                    private static void pArray(int[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static void pArray(long[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static void pArray(boolean[] arr) {
                        for (int i = 0; i < arr.length; i++) {
                            pw.print(arr[i] + " ");
                        }
                        pw.println();
                        return;
                    }
 
                    private static boolean isSpaceChar(int c) {
                        if (filter != null)
                            return filter.isSpaceChar(c);
                        return isWhitespace(c);
                    }
 
                    private interface SpaceCharFilter {
                        public boolean isSpaceChar(int ch);
                    }
                    

}