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. 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 . 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. 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.