Squads

Peter is playing with his toy soldiers, lining them up side by side. He wants to form squads from them, where within each squad, everyone except the commander has a direct superior. He will use the experience points of the soldiers ( $x_{i} \ \ i=1\ldots N$ ) as follows: for each soldier ( $x_{i}$ ), he assigns as a superior the closest, more experienced soldier among those located either in the negative or positive direction ( $d_{i}$ ).

Of course, if no such soldier exists in the respective direction, no one is assigned as their superior. In this way, one or more squads are formed. The experience points of a squad are defined as the sum of the experience points of its members, which Péter also refers to as the squad’s strength.

Examples:

I.
x: 8 6 4 3 9 2 5 7
d: - + - + - + + +

  squad                            experience
  8                                         8
  3,4,6,9                                  22
  2,5,7                                    14


II.
The soldiers' experience points are not necessarily unique!
In such cases, the soldiers are referred to by their indices instead of their experience points.

x: 10  8  6  4  3  9  2  5  7   5   9
d:  +  -  -  +  +  -  +  -  +   +   +
i:  1  2  3  4  5  6  7  8  9  10  11


  squad                           experience
  1,2,3,4,5,6,7,8                         47
  9,10,11                                 21

Input specification

The first line contains the number of soldiers, $N$ . The second line lists the soldiers’ experience points, $x_{i}\ \ i=1,\ldots,N$ , separated by spaces. The third line contains the directions, $d_{i}\in\{-,+\}\ \ i=1,\ldots,N$ , also separated by spaces.