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J. Bottles
time limit per test
2 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

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

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 a 1, a 2, ..., a n (1 ≤ a i ≤ 100), where a i is the amount of soda remaining in the i-th bottle.

The third line contains n positive integers b 1, b 2, ..., b n (1 ≤ b i ≤ 100), where b i is the volume of the i-th bottle.

It is guaranteed that a i ≤ b i 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
43 3 4 34 7 6 5
Output
2 6
Input
21 1100 100
Output
1 1
Input
510 30 5 6 2410 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.