Nick has n bottles of soda left after his birthday. Each bottle is described by two values: remaining amount of soda ai and bottle volume bi (ai ≤ bi).

Nick has decided to pour all remaining soda into minimal number of bottles, moreover he has to do it as soon as possible. Nick spends x seconds to pour x units of soda from one bottle to another.

Nick asks you to help him to determine k — the minimal number of bottles to store all remaining soda and t — the minimal time to pour soda into k bottles. A bottle can't store more soda than its volume. All remaining soda should be saved.

Input

The first line contains positive integer n (1 ≤ n ≤ 100) — the number of bottles.

The second line contains n positive integers a1, a2, ..., an (1 ≤ ai ≤ 100), where ai is the amount of soda remaining in the i-th bottle.

The third line contains n positive integers b1, b2, ..., bn (1 ≤ bi ≤ 100), where bi is the volume of the i-th bottle.

It is guaranteed that ai ≤ bi for any i.

Output

The only line should contain two integers k and t, where k is the minimal number of bottles that can store all the soda and t is the minimal time to pour the soda into k bottles.

Examples

Input

4
3 3 4 3
4 7 6 5


Output

2 6


Input

2
1 1
100 100


Output

1 1


Input

5
10 30 5 6 24
10 41 7 8 24


Output

3 11

Note

In the first example Nick can pour soda from the first bottle to the second bottle. It will take 3 seconds. After it the second bottle will contain 3 + 3 = 6 units of soda. Then he can pour soda from the fourth bottle to the second bottle and to the third bottle: one unit to the second and two units to the third. It will take 1 + 2 = 3 seconds. So, all the soda will be in two bottles and he will spend 3 + 3 = 6 seconds to do it.
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 * 
 * @author pttrung
 */
public class J_NEERC_2016 {

	public static long MOD = 1000000007;

	public static void main(String[] args) throws FileNotFoundException {
		// PrintWriter out = new PrintWriter(new FileOutputStream(new File(
		// "output.txt")));
		PrintWriter out = new PrintWriter(System.out);
		Scanner in = new Scanner();
		int n = in.nextInt();
		int[][] data = new int[n][2];
		int total = 0;
		for (int j = 0; j < 2; j++) {
			for (int i = 0; i < n; i++) {
				data[i][j] = in.nextInt();
				if (j == 0) {
					total += data[i][j];
				}
			}

		}
		int[][][] dp = new int[n + 1][2][n * 100 + 1];
		for (int[][] a : dp) {
			for (int[] b : a) {
				Arrays.fill(b, -1);
			}
		}
		dp[0][1][0] = 0;
		for (int i = 0; i < n; i++) {
			int[][][] nxt = new int[n + 1][2][n * 100 + 1];
			for (int[][] a : nxt) {
				for (int[] b : a) {
					Arrays.fill(b, -1);
				}
			}
			for (int j = i; j >= 0; j--) {
				for (int k = 0; k <= n * 100; k++) {
					if (dp[j][0][k] != -1) {
						// Not use this bottle
						if (nxt[j][0][k + data[i][0]] == -1
								|| nxt[j][0][k + data[i][0]] > dp[j][0][k]
										+ data[i][0]) {
							nxt[j][0][k + data[i][0]] = dp[j][0][k]
									+ data[i][0];
						}
						// Use this bottle;
						int have = data[i][1] - data[i][0];
						if (have >= k) {
							if (nxt[j + 1][1][have - k] == -1
									|| nxt[j + 1][1][have - k] > dp[j][0][k]) {
								nxt[j + 1][1][have - k] = dp[j][0][k];
							}
						} else {
							if (nxt[j + 1][0][k - have] == -1
									|| nxt[j + 1][0][k - have] > dp[j][0][k]) {
								nxt[j + 1][0][k - have] = dp[j][0][k];
							}
						}
					}
					if (dp[j][1][k] != -1) {
						// Not use this bottle
						if (k < data[i][0]) {
							if (nxt[j][0][data[i][0] - k] == -1
									|| nxt[j][0][data[i][0] - k] > dp[j][1][k]
											+ data[i][0]) {
								nxt[j][0][data[i][0] - k] = dp[j][1][k]
										+ data[i][0];
							}
						} else {
							if (nxt[j][1][k - data[i][0]] == -1
									|| nxt[j][1][k - data[i][0]] > dp[j][1][k]
											+ data[i][0]) {
								nxt[j][1][k - data[i][0]] = dp[j][1][k]
										+ data[i][0];
							}
						}
						// Use this bottle;
						int have = data[i][1] - data[i][0];

						if (nxt[j + 1][1][have + k] == -1
								|| nxt[j + 1][1][have + k] > dp[j][1][k]) {
							nxt[j + 1][1][have + k] = dp[j][1][k];
						}

					}
				}
			}
			
			dp = nxt;
		}
		boolean found = false;
		for(int i = 0; i <= n && !found; i++){
			int max = Integer.MAX_VALUE;
			for(int j = 0;j <= 100*n; j++){
				if(dp[i][1][j] != -1){
					found = true;
					max = Math.min(max, dp[i][1][j]);
				}
			}
			if(found){
				out.println(i + " " + max);
			}
		}

		out.close();
	}

	public static int[] KMP(String val) {
		int i = 0;
		int j = -1;
		int[] result = new int[val.length() + 1];
		result[0] = -1;
		while (i < val.length()) {
			while (j >= 0 && val.charAt(j) != val.charAt(i)) {
				j = result[j];
			}
			j++;
			i++;
			result[i] = j;
		}
		return result;

	}

	public static boolean nextPer(int[] data) {
		int i = data.length - 1;
		while (i > 0 && data[i] < data[i - 1]) {
			i--;
		}
		if (i == 0) {
			return false;
		}
		int j = data.length - 1;
		while (data[j] < data[i - 1]) {
			j--;
		}
		int temp = data[i - 1];
		data[i - 1] = data[j];
		data[j] = temp;
		Arrays.sort(data, i, data.length);
		return true;
	}

	public static int digit(long n) {
		int result = 0;
		while (n > 0) {
			n /= 10;
			result++;
		}
		return result;
	}

	public static double dist(long a, long b, long x, long y) {
		double val = (b - a) * (b - a) + (x - y) * (x - y);
		val = Math.sqrt(val);
		double other = x * x + a * a;
		other = Math.sqrt(other);
		return val + other;

	}

	public static class Point implements Comparable<Point> {

		int x, y;

		public Point(int start, int end) {
			this.x = start;
			this.y = end;
		}

		@Override
		public int hashCode() {
			int hash = 5;
			hash = 47 * hash + this.x;
			hash = 47 * hash + this.y;
			return hash;
		}

		@Override
		public boolean equals(Object obj) {
			if (obj == null) {
				return false;
			}
			if (getClass() != obj.getClass()) {
				return false;
			}
			final Point other = (Point) obj;
			if (this.x != other.x) {
				return false;
			}
			if (this.y != other.y) {
				return false;
			}
			return true;
		}

		@Override
		public int compareTo(Point o) {
			return Integer.compare(x, o.x);
		}
	}

	public static class FT {

		long[] data;

		FT(int n) {
			data = new long[n];
		}

		public void update(int index, long value) {
			while (index < data.length) {
				data[index] += value;
				index += (index & (-index));
			}
		}

		public long get(int index) {
			long result = 0;
			while (index > 0) {
				result += data[index];
				index -= (index & (-index));
			}
			return result;

		}
	}

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

	public static long pow(long a, long b) {
		if (b == 0) {
			return 1;
		}
		if (b == 1) {
			return a;
		}
		long val = pow(a, b / 2);
		if (b % 2 == 0) {
			return val * val % MOD;
		} else {
			return val * (val * a % MOD) % MOD;

		}
	}

	static class Scanner {

		BufferedReader br;
		StringTokenizer st;

		public Scanner() throws FileNotFoundException {
			// System.setOut(new PrintStream(new
			// BufferedOutputStream(System.out), true));
			br = new BufferedReader(new InputStreamReader(System.in));
			// br = new BufferedReader(new InputStreamReader(new
			// FileInputStream(new File("input.txt"))));
		}

		public String next() {

			while (st == null || !st.hasMoreTokens()) {
				try {
					st = new StringTokenizer(br.readLine());
				} catch (Exception e) {
					throw new RuntimeException();
				}
			}
			return st.nextToken();
		}

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

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

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

		public String nextLine() {
			st = null;
			try {
				return br.readLine();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}

		public boolean endLine() {
			try {
				String next = br.readLine();
				while (next != null && next.trim().isEmpty()) {
					next = br.readLine();
				}
				if (next == null) {
					return true;
				}
				st = new StringTokenizer(next);
				return st.hasMoreTokens();
			} catch (Exception e) {
				throw new RuntimeException();
			}
		}
	}
}
