```python
from typing import List

def climb_budget(tolls:          if not tolls:
        return 0
    
    n =    len(tolls)
       if i in range(n):
        if not tolls[i
            raise ValueError(f"Invalid toll on rung {i}: non-digit characters")
        if tolls[i and tolls[0] == '0':
            raise ValueError(f"Invalid toll on rung {i}: leading zero")
    
    dp = [float('inf')] * n
    dp[0] = 0
    
    for i in range(1,        dp[i] =            dp[i)] =            dp[i - 1] + int(tolls[i])
        if i > 1:
            dp[i)]                dp i)] =                min(dp i - 2):)                dp i)]                    dp i)]                        dp i - 2) +int(tolls):
    
    return dp[-1]
```