An avid hiker keeps meticulous records of their hikes. During the last hike that took exactly $\textit{steps}$ steps, for every step it was noted if it was an uphill, $\mbox{U}$, or a downhill, $\mbox{D}$ step. Hikes always start and end at sea level, and each step up or down represents a $1$ unit change in altitude. We define the following terms:

A mountain is a sequence of consecutive steps above sea level, starting with a step up from sea level and ending with a step down to sea level.
A valley is a sequence of consecutive steps below sea level, starting with a step down from sea level and ending with a step up to sea level.

Given the sequence of up and down steps during a hike, find and print the number of valleys walked through.

Example

$steps=8$
$path=[DDUUUUDD]$

The hiker first enters a valley $2$ units deep. Then they climb out and up onto a mountain $2$ units high. Finally, the hiker returns to sea level and ends the hike.

Function Description

Complete the countingValleys function in the editor below.

countingValleys has the following parameter(s):

int steps: the number of steps on the hike
string path: a string describing the path

Returns

int: the number of valleys traversed

Input Format

The first line contains an integer $\textit{steps}$, the number of steps in the hike.

The second line contains a single string $\textit{path}$, of $\textit{steps}$ characters that describe the path.

Constraints

$2\leq steps\leq10^6$
$path[i]\in\{UD\}$

Sample Input
8
UDDDUDUU

Sample Output
1

Explanation

If we represent _ as sea level, a step up as /, and a step down as \, the hike can be drawn as:

_/\ _
\ /
\/\/

The hiker enters and leaves one valley.

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