There are obstacles placed in a field. Your task is to design a course that visits each obstacle exactly once, in any order, following a straight line between consecutive obstacles, without ever crossing itself.

The catch? The sequence of turn directions (left or right) has already been decided, in a string of length . If the th character of the turn sequence is `L`

, then the locations of the th, th, and th obstacles, in that order must form a counterclockwise angle. If it is `R`

, they must form a clockwise angle.

#### Input

The first line of input contains a single integer .

Each of the next lines contains two space-separated integers and , giving the coordinates of obstacle .

The next and final line contains a single string with exactly characters consisting of only `L`

and `R`

, representing the sequence of turn directions.

It is guaranteed that no three obstacles will be collinear.

#### Output

If no solution is possible, print, on a single line, the integer `-1`

. Otherwise, print, on a single line, any permutation of the obstacles that satisfies the requirements. The permutation should be given as distinct space-separated integers with , and this ordering of the points should satisfy the turn directions indicated by the turn sequence.

If there are multiple possible solutions, print any of them.

#### Sample Input

```
4
2 2
2 1
1 2
1 1
LR
```

#### Sample Output

`1 3 2 4`

## Comments