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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.InputMismatchException;
import java.util.StringTokenizer;
/*
 * 
 * daiict
 *
 * 
 * 
 */

public class pprac
{
	FastScanner in;
	PrintWriter out;

	static int countc = 0;
	static int minm = countc;

	static ArrayList[] adj;
	static ArrayList[] aadj;
	static int last;
	static int n;
	static int m;

	static int[] dp1;
	static int[] dp2;
	static int color[];
	static int visited[];
	static int[] arr;
	static long[] brr;
	static double ans;
	static int array[];
	static int start[];
	static int finish[];
	static int pref[];
	static int tree[];
	static int maxval = 32;

	static int ttt[];
	static int sum = 0;
	static String s;

	static int cc = 0;
	static long min = Long.MAX_VALUE;

	static ArrayList<Integer> segt[];

	// for dfs do not delete
	static int dir[][] =
	{
			{ 1, 0 },
			{ 0, 1 },
			{ 0, -1 },
			{ -1, 0 } };

	static int[] seg;
	static long count = 1;
	static long mod = (long) 1e9 + 7;

	static int parent[];
	static int size[];

	static int[] l;
	static int[] r;
	static int[] next;
	static int[] cnt;
	static int[] block;

	static int bblock = 1001;

	static HashSet<String> set;
	static HashSet<String> set2;

	static int low[];
	static int disc[];
	static int time;
	static int acn[];

	static HashMap<Long, Integer> map;

	static class Pair implements Comparable<Pair>
	{
		int x;
		int y;
		int i;

		Pair(int l, int m, int i)
		{

			this.x = l;
			this.y = m;
			this.i = i;

		}

		public int compareTo(Pair p)
		{

			if (this.x / bblock == p.x / bblock)
			{
				return (int) (this.y - p.y);
			}
			return (int) (this.x / bblock - p.x / bblock);
		}

		public String toString()
		{
			return x + " " + y;
		}

		public boolean equals(Object o)
		{
			if (o instanceof Pair)
			{
				Pair a = (Pair) o;

				return this.x == a.x;
			}

			return false;
		}

		public int hashCode()
		{
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}

	}

	public static int gcd(int a, int b)
	{
		if (b == 0)
			return a;
		return gcd(b, a % b);
	}

	void build(int n)
	{ // build the tree
		for (int i = n - 1; i > 0; --i)
			seg[i] = Math.min(seg[i << 1], seg[i << 1 | 1]);
	}

	public static void modify(int p, int val, int n)
	{ // set value at position
		// p
		for (seg[p += n] = val; p > 1; p >>= 1)
			seg[p >> 1] = Math.min(seg[p], seg[p ^ 1]);
	}

	int query(int l, int r, int n)
	{ // sum on interval [l, r)
		int res = Integer.MAX_VALUE;

		if (l > r)
		{
			return res;
		}

		for (l += n, r += n; l < r; l >>= 1, r >>= 1)
		{
			if ((l & 1) == 1)
				res = Math.min(res, seg[l++]);
			if ((r & 1) == 1)
				res = Math.min(res, seg[--r]);
		}
		return res;
	}

	// public static void update(int x,int val){
	// while(x<=maxval){
	// tree[x] += val;
	// x = (x&-x);
	// }
	// }

	public static int read(int idx)
	{
		int sum = 0;

		while (idx >= 0)
		{
			sum += tree[idx];
			idx -= (idx & (-idx));
		}

		return sum;
	}

	public static int find(int i)
	{
		if (parent[i] != i)
		{
			return find(parent[i]);
		}

		return i;
	}

	public static void union(int a, int b)
	{
		int x = find(a);
		int y = find(b);

		if (x != y)
		{
			if (size[x] > size[y])
			{
				size[x] += size[y];
				parent[y] = x;
			} else
			{
				size[y] += size[x];
				parent[x] = y;
			}
		}
	}

			/* static */ void solve() throws NumberFormatException, InputMismatchException, IOException
	{

		// Scanner in = new Scanner(System.in);

		int n = in.nextInt();
		int k = in.nextInt() + in.nextInt();

		int arr[] = new int[n];

		for (int i = 0; i < n; i++)
		{
			arr[i] = in.nextInt();
		}

		int brr[] = new int[n];

		for (int i = 0; i < n; i++)
		{
			brr[i] = in.nextInt();
		}

		long crr[] = new long[n];

		for (int i = 0; i < n; i++)
		{
			crr[i] = (long)Math.abs(arr[i] - brr[i]);
		}

		while (k > 0)
		{

			Arrays.sort(crr);
			if (crr[n - 1] == 0)
			{
				crr[n - 1] = -1;
				k--;

				if (k % 2 == 0)
				{
					crr[n - 1] = -1;
				} else
				{
					crr[n - 1] = 0;
				}

				k = 0;
				break;
			} else
			{
				crr[n - 1]--;
				k--;
			}

		}

		long ans = 0;
		for (int i = 0; i < n; i++)
		{
			ans += crr[i] * crr[i];
		}

		out.println(ans);

	}

	public static int call(char arr[][])
	{
		int cc = 0;

		char temp[][] = new char[arr.length][arr.length];

		char c = '0';

		for (int i = 0; i < arr.length; i++)
		{
			c = (c == '0') ? '1' : '0';
			for (int j = 0; j < arr.length; j++)
			{
				temp[i][j] = c;
				c = (c == '0') ? '1' : '0';
				// System.out.print(temp[i][j]);
			}
			// System.out.println();
		}

		int n = arr.length;
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < n; j++)
			{
				if (arr[i][j] != temp[i][j])
				{
					cc++;
				}
			}
		}

		int dd = cc;

		cc = 0;

		c = '1';

		for (int i = 0; i < arr.length; i++)
		{
			c = (c == '0') ? '1' : '0';
			for (int j = 0; j < arr.length; j++)
			{
				temp[i][j] = c;
				c = (c == '0') ? '1' : '0';
			}
		}

		n = arr.length;
		for (int i = 0; i < n; i++)
		{
			for (int j = 0; j < n; j++)
			{
				if (arr[i][j] != temp[i][j])
				{
					cc++;
				}
			}
		}

		return Math.min(cc, dd);

	}

	public static HashSet<Integer> call(int a)
	{

		HashSet<Integer> list = new HashSet();

		while (a % 2 == 0)
		{
			list.add(2);
			a /= 2;
		}
		int n = a;
		for (int i = 3; i <= n; i += 2)
		{
			while (a % i == 0)
			{
				list.add(i);
				a = a / i;
			}
		}

		if (a > 2)
		{
			list.add(a);
		}

		return list;
	}

	public static String reverse(String s)
	{

		String ans = "";

		for (int i = s.length() - 1; i >= 0; i--)
		{
			ans += s.charAt(i);
		}

		return ans;

	}

	public static long sum(long x)
	{
		return x < 10 ? x : x % 10 + sum(x / 10);
	}

	public static long gcd(long x, long y)
	{
		if (x == 0)
			return y;
		else
			return gcd(y % x, x);
	}

	static long inv(long x, long mod)
	{
		long r, y;
		for (r = 1, y = mod - 2; y != 0; x = x * x % mod, y >>= 1)
		{
			if ((y & 1) == 1)
				r = r * x % mod;

		}
		return r;
	}

	public static long pow(long x, long y, long n)
	{
		if (y == 0)
			return 1 % n;
		if (y % 2 == 0)
		{
			long z = pow(x, y / 2, n);
			return (z * z) % n;
		}
		return ((x % n) * pow(x, y - 1, n)) % n;
	}

	public static boolean isPrime(long a)
	{
		// Corner cases
		if (a <= 1)
			return false;
		if (a <= 3)
			return true;

		// This is checked so that we can skip
		// middle five numbers in below loop
		if (a % 2 == 0 || a % 3 == 0)
			return false;

		for (long i = 5; i * i <= a; i = i + 6)
			if (a % i == 0 || a % (i + 2) == 0)
				return false;

		return true;
	}

	void run() throws NumberFormatException, InputMismatchException, IOException
	{
		in = new FastScanner();
		out = new PrintWriter(System.out);

		solve();

		out.close();
	}

	class FastScanner
	{
		BufferedReader br;
		StringTokenizer st;

		public FastScanner()
		{
			br = new BufferedReader(new InputStreamReader(System.in));
		}

		String next()
		{
			while (st == null || !st.hasMoreTokens())
			{
				try
				{
					st = new StringTokenizer(in.br.readLine());
				} catch (IOException e)
				{
					// TODO Auto-generated catch block
					e.printStackTrace();
				}
			}
			return st.nextToken();
		}

		int nextInt()
		{
			return Integer.parseInt(next());
		}

		long nextLong()
		{
			return Long.parseLong(next());
		}

		double nextDouble()
		{
			return Double.parseDouble(next());
		}
	}

	public static void main(String[] args) throws NumberFormatException, InputMismatchException, IOException
	{
		// new Thread(null ,new Runnable(){
		// public void run(){
		// try{
		//
		// test();
		//
		// } catch(Exception e){
		// e.printStackTrace();
		// }
		// }
		// },"1",1<<26).start();
		// }
		// static StringBuilder sb;
		// public static void test() throws IOException{
		// sb=new StringBuilder();
		// int t=1;
		// while(t-->0){
		//
		// solve();
		//
		// }
		//

		new pprac().run();
	}

}

class Node
{
	int a;
	int b;

	public Node(int i, int j)
	{
		this.a = i;
		this.b = j;

	}

}

class MyComp implements Comparator<String>
{

	int c = 0;

	MyComp(int d)
	{
		c = d;
	}

	@Override
	public int compare(String a, String b)
	{

		// < == -1

		String arr[] = a.split(" ");
		String brr[] = b.split(" ");

		return arr[c].compareTo(brr[c]);

	}

}

class MyComp2 implements Comparator<Node>
{

	@Override
	public int compare(Node a, Node b)
	{

		// < == -1

		if (a.b > b.b)
		{
			return -1;
		} else
		{
			return 1;
		}

	}

}