You are given three multisets of pairs of colored sticks: 

  * R pairs of red sticks, the first pair has length r_1, the second pair has length r_2, ..., the R-th pair has length r_R; 
  * G pairs of green sticks, the first pair has length g_1, the second pair has length g_2, ..., the G-th pair has length g_G; 
  * B pairs of blue sticks, the first pair has length b_1, the second pair has length b_2, ..., the B-th pair has length b_B; 



You are constructing rectangles from these pairs of sticks with the following process: 

  1. take a pair of sticks of one color; 
  2. take a pair of sticks of another color different from the first one; 
  3. add the area of the resulting rectangle to the total area. 



Thus, you get such rectangles that their opposite sides are the same color and their adjacent sides are not the same color.

Each pair of sticks can be used at most once, some pairs can be left unused. You are not allowed to split a pair into independent sticks.

What is the maximum area you can achieve?

Input

The first line contains three integers R, G, B (1 ≤ R, G, B ≤ 200) — the number of pairs of red sticks, the number of pairs of green sticks and the number of pairs of blue sticks.

The second line contains R integers r_1, r_2, ..., r_R (1 ≤ r_i ≤ 2000) — the lengths of sticks in each pair of red sticks.

The third line contains G integers g_1, g_2, ..., g_G (1 ≤ g_i ≤ 2000) — the lengths of sticks in each pair of green sticks.

The fourth line contains B integers b_1, b_2, ..., b_B (1 ≤ b_i ≤ 2000) — the lengths of sticks in each pair of blue sticks.

Output

Print the maximum possible total area of the constructed rectangles.

Examples

Input


1 1 1
3
5
4


Output


20


Input


2 1 3
9 5
1
2 8 5


Output


99


Input


10 1 1
11 7 20 15 19 14 2 4 13 14
8
11


Output


372

Note

In the first example you can construct one of these rectangles: red and green with sides 3 and 5, red and blue with sides 3 and 4 and green and blue with sides 5 and 4. The best area of them is 4 × 5 = 20.

In the second example the best rectangles are: red/blue 9 × 8, red/blue 5 × 5, green/blue 2 × 1. So the total area is 72 + 25 + 2 = 99.

In the third example the best rectangles are: red/green 19 × 8 and red/blue 20 × 11. The total area is 152 + 220 = 372. Note that you can't construct more rectangles because you are not allowed to have both pairs taken to be the same color.

import java.io.*;
import java.util.*;

import java.math.*;

public class Main {

	// static long sx = 0, sy = 0, mod = (long) (998244353);

	static ArrayList<Integer>[] a;
	static ArrayList<Long> p;
	static Long[][][] dp;
	static HashMap<ArrayList<Integer>, Long> hm = new HashMap<>();
	static boolean[][] vis;
	static int[] farr;
	static long[] far;
	public static PrintWriter out = new PrintWriter(System.out);
	static ArrayList<pair> pa = new ArrayList<>();
	static long[] fact = new long[(int) 1e6];
	static StringBuilder sb = new StringBuilder();
	static boolean cycle = false;
	static long mo = (long) (1e9 + 7);
	static int[] c, col;
	// static int n = 0, m, x, k;
	static int ans = Integer.MAX_VALUE;
	static boolean b = true;
	static boolean[] reach = new boolean[6000];
	static int[][] par;
	static int[] depth;
	static int[] size;
	static long[] pow;
	static int time = 0;
	static int[] disc;
	static int[] low;
	static char[][] ch;
	// static int cnt = 0;
	static int[][] dirs = { { -1, 0 }, { 0, 1 }, { 1, 0 }, { 0, -1 }, };
	static int n = 0, k = 0, z = 0;
	// static long[] p;
	static long[] h;
	static String s1, s2;
	static long x, y;

	public static void main(String[] args) throws IOException {

		// Scanner scn = new Scanner(new BufferedReader(new
		// InputStreamReader(System.in)));

		Reader scn = new Reader();

		int n = scn.nextInt(), m = scn.nextInt(), r = scn.nextInt();

		long[] a = new long[n + 1];
		
		dp = new Long[n+1][m+1][r+1];

		for (int i = 1; i <= n; i++)
			a[i] = scn.nextLong();

		long[] b = new long[m + 1];

		for (int i = 1; i <= m; i++)
			b[i] = scn.nextLong();

		long[] c = new long[r + 1];

		for (int i = 1; i <= r; i++)
			c[i] = scn.nextLong();

		Arrays.sort(a, 1, n + 1);
		Arrays.sort(b, 1, m + 1);
		Arrays.sort(c, 1, r + 1);

		long ans = f(a, b, c, n, m, r);
		System.out.println(ans);

	}

	private static long f(long[] a, long[] b, long[] c, int i, int j, int k) {

		long ans = 0;
		
		if(dp[i][j][k]!=null)
			 return dp[i][j][k];

		if (i > 0 && j > 0)
			ans = f(a, b, c, i - 1, j - 1, k) + a[i] * b[j];

		if (i > 0 && k > 0)
			ans = Math.max(ans, f(a, b, c, i - 1, j, k - 1) + a[i] * c[k]);

		if (j > 0 && k > 0)
			ans = Math.max(ans, f(a, b, c, i, j - 1, k - 1) + b[j] * c[k]);

		return dp[i][j][k] = ans;
	}

	// _________________________TEMPLATE_____________________________________________________________

	// public static long lcm(long x, long y) {
	//
	// return (x * y) / gcd(x, y);
	// }
	//
	// private static long gcd(long x, long y) {
	// if (x == 0)
	// return y;
	//
	// return gcd(y % x, x);
	// }

	//
	// static class comp implements Comparator<Integer> {
	//
	// @Override
	// public int compare(Integer p1, Integer p2) {
	//
	// return p2 - p1;
	//
	// }
	// }
	//
	// }
	//
	// public static long pow(long a, long b, long mod) {
	//
	// if (b < 0)
	// return 0;
	// if (b == 0 || b == 1)
	// return (long) Math.pow(a, b);
	//
	// if (b % 2 == 0) {
	//
	// long ret = pow(a, b / 2, mod);
	// ret = (ret % mod * ret % mod) % mod;
	// return ret;
	// }
	//
	// else {
	// return ((pow(a, b - 1, mod) % mod) * a % mod) % mod;
	// }
	// }

	private static class pair implements Comparable<pair> {

		int i;
		int val;

		pair(int c, int d) {
			i = c;
			val = d;
		}

		@Override
		public int compareTo(pair o) {

			return o.val - this.val;
		}

		// @Override
		//
		// public int hashCode() {
		// return i;
		// }
		//
		// @Override
		//
		// public boolean equals(Object o) {
		//
		// pair p = (pair) o;
		// return this.i == p.i;
		// }

	}

	private static class pair1 {

		int a, b;

		pair1(int a, int b) {
			this.a = a;
			this.b = b;
		}

	}

	private static String reverse(String s) {

		return new StringBuilder(s).reverse().toString();
	}

	public static class Reader {
		final private int BUFFER_SIZE = 1 << 16;
		private DataInputStream din;
		private byte[] buffer;
		private int bufferPointer, bytesRead;

		public Reader() {
			din = new DataInputStream(System.in);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public Reader(String file_name) throws IOException {
			din = new DataInputStream(new FileInputStream(file_name));
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String readLine() throws IOException {
			byte[] buf = new byte[1000000 + 1]; // line length
			int cnt = 0, c;
			while ((c = read()) != -1) {
				if (c == '\n')
					break;
				buf[cnt++] = (byte) c;
			}
			return new String(buf, 0, cnt);
		}

		public int nextInt() throws IOException {
			int ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (neg)
				return -ret;
			return ret;
		}

		public long nextLong() throws IOException {
			long ret = 0;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();
			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');
			if (neg)
				return -ret;
			return ret;
		}

		public double nextDouble() throws IOException {
			double ret = 0, div = 1;
			byte c = read();
			while (c <= ' ')
				c = read();
			boolean neg = (c == '-');
			if (neg)
				c = read();

			do {
				ret = ret * 10 + c - '0';
			} while ((c = read()) >= '0' && c <= '9');

			if (c == '.') {
				while ((c = read()) >= '0' && c <= '9') {
					ret += (c - '0') / (div *= 10);
				}
			}

			if (neg)
				return -ret;
			return ret;
		}

		private void fillBuffer() throws IOException {
			bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			if (bytesRead == -1)
				buffer[0] = -1;
		}

		private byte read() throws IOException {
			if (bufferPointer == bytesRead)
				fillBuffer();
			return buffer[bufferPointer++];
		}

		public void close() throws IOException {
			if (din == null)
				return;
			din.close();
		}

		public int[] nextIntArray(int n) throws IOException {
			int[] arr = new int[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextInt();
			}
			return arr;
		}

		public long[] nextLongArray(int n) throws IOException {
			long[] arr = new long[n];
			for (int i = 0; i < n; i++) {
				arr[i] = nextLong();
			}
			return arr;
		}

		public int[][] nextInt2DArray(int m, int n) throws IOException {
			int[][] arr = new int[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}

		public long[][] nextInt2DArrayL(int m, int n) throws IOException {
			long[][] arr = new long[m][n];
			for (int i = 0; i < m; i++) {
				for (int j = 0; j < n; j++)
					arr[i][j] = nextInt();
			}
			return arr;
		}
		// kickstart - Solution
		// atcoder - Main
	}

}