Water held between bars

Question

Bars of width one stand along a line at the given heights. Return how many units of water stay trapped between them after it rains.

```python
def solve(raw: str) -> str:
    ...


def run_case(case: dict) -> str:
    return solve(case["stdin"])
```

## Requirements

- Line 1 is the bar count; line 2 lists the height of each bar from left to right.
- The water above a bar is bounded by the shorter of the tallest bars on its left and on its right, minus the bar's own height.
- Bars at the two ends hold nothing, and a stretch that only falls or only rises holds nothing.
- Return the total as a decimal string with no per-bar breakdown and no trailing newline.
- Heights are non-negative integers; the total fits in ordinary integer arithmetic.
- An input with zero or one bar traps nothing.