For her current programming project, Soriya needs to first construct the array which has length . However, to entertain herself, she decides to add the elements in the order described by the permutation . That is, for her th insertion, she will add the element to its position in the array. Since Soriya has nothing better to do with her life, she wonders: how many inversions will the array have after each insertion? An inversion is a pair of indices such that and .

#### Input Specification

The first line contains the positive integer .

The second line consists of positive integers, the array .

The third line consists of positive integers, the permutation .

#### Output Specification

Output lines, the th of which containing a single integer, the number of inversions after Soriya adds her th element.

#### Constraints

In all subtasks,

##### Subtask 1 [15%]

for

##### Subtask 2 [25%]

##### Subtask 3 [60%]

No additional constraints

#### Sample Input 1

```
5
4 3 1 2 3
1 2 3 4 5
```

#### Sample Output 1

```
0
1
3
5
6
```

#### Sample Input 2

```
5
4 3 1 2 3
3 5 1 4 2
```

#### Sample Output 2

```
0
0
2
3
6
```

## Comments