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.InputStreamReader;

public class A {
	static int n, a[], b[];
	static int dp[][][] = new int[100][20000 + 5][];
	static int offset = 10000;

	static int[] go(int curr, int have) {
		if (curr >= n) {
			return have >= 0 ? new int[] { 0, 0 } : new int[] { -1, -1 };
		}
		if (dp[curr][have + offset] != null)
			return dp[curr][have + offset];
		int[] ans = go(curr + 1, have + b[curr] - a[curr]).clone();
		if (ans[0] != -1) {
			ans[0]++;
		}
		int[] ans2 = go(curr + 1, have - a[curr]).clone();
		if (ans2[0] != -1) {
			ans2[1] += a[curr];
			if (ans2[0] < ans[0] || (ans2[0] == ans[0] && ans2[1] < ans[1])) {
				ans = ans2;
			}
		}
		return dp[curr][have + offset] = ans;
	}

	public static void main(String[] args) throws Exception {
		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
		String l[];
		n = Integer.parseInt(bf.readLine());
		l = bf.readLine().split(" ");
		a = new int[n];
		for (int i = 0; i < a.length; i++) {
			a[i] = Integer.parseInt(l[i]);
		}
		l = bf.readLine().split(" ");
		b = new int[n];
		for (int i = 0; i < a.length; i++) {
			b[i] = Integer.parseInt(l[i]);
		}
		int ans[] = go(0, 0);
		System.out.println(ans[0] + " " + ans[1]);
	}
}