Bob is biking on a trail with sections. This trail has uphills, downhills, and flat sections, denoted by `U`

, `D`

, and `F`

, respectively. He starts with a speed of , and will bike through the entire trail. When **biking**:

- On uphill sections, Bob will lose unit of speed.
- On downhill sections, Bob will gain unit of speed.
- On flat sections, Bob's speed will not change.

If Bob's speed becomes , he will have to get off his bike and walk **until** he reaches either a downhill section or the end of the trail. His speed cannot be negative.

How many total sections will Bob have to walk on?

#### Constraints

#### Input Specification

The first line will contain two space-separated integers and .

The second and final line will contain a string of length with only the characters `U`

, `D`

, and `F`

.

#### Output Specification

Output one integer on one line, the number of sections Bob will have to walk on.

#### Sample Input

```
11 1
FUDDDUDUUUF
```

#### Sample Output

`3`

#### Explanation

Bob has to walk the second section and from the tenth section to the end of the trail, as in these sections, his speed is .

## Comments