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.
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.
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.
4
3 3 4 3
4 7 6 5
2 6
2
1 1
100 100
1 1
5
10 30 5 6 24
10 41 7 8 24
3 11
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.