Problem: Valley Count in a Number Path

Problem: Valley Count in a Number Path

You are given a list of integers that represent steps going up or down on a path.

Rules

The path always starts at height 0.

Each number in the list tells how much the height changes at that step.

Positive → go up   
Negative → go down

A valley is counted when:

You go below height 0, and       
Later return back to height 0.

Your task: Count how many valleys happen in the path.

Input

A list of integers (at least one value).

Output

A single integer: the number of valleys.

e.g.

Example 1

Input: [1, -2, -1, 2]

Explanation (not a hint, just clarity of the sample):
The path goes below 0 and comes back — that is 1 valley.

Output: 1

Example 2

Input: [-1, -1, 2, -3, 3]

Output: 2