There is a one-dimensional garden on the x-axis. The garden starts at the point 0 and ends at the point n. (i.e The length of the garden is n).
There are n + 1 taps located at points [0, 1, ..., n] in the garden.
Given an integer n and an integer array ranges of length n + 1 where ranges[i] (0-indexed) means the i-th tap can water the area [i - ranges[i], i + ranges[i]] if it was open.
Return the minimum number of taps that should be open to water the whole garden, If the garden cannot be watered return -1.
 
Example 1:

Input: n = 5, ranges = [3,4,1,1,0,0]
Output: 1
Explanation: The tap at point 0 can cover the interval [-3,3]
The tap at point 1 can cover the interval [-3,5]
The tap at point 2 can cover the interval [1,3]
The tap at point 3 can cover the interval [2,4]
The tap at point 4 can cover the interval [4,4]
The tap at point 5 can cover the interval [5,5]
Opening Only the second tap will water the whole garden [0,5]

Example 2:
Input: n = 3, ranges = [0,0,0,0]
Output: -1
Explanation: Even if you activate all the four taps you cannot water the whole garden.

Example 3:
Input: n = 7, ranges = [1,2,1,0,2,1,0,1]
Output: 3

Example 4:
Input: n = 8, ranges = [4,0,0,0,0,0,0,0,4]
Output: 2

Example 5:
Input: n = 8, ranges = [4,0,0,0,4,0,0,0,4]
Output: 1

 
Constraints:

1 <= n <= 10^4
ranges.length == n + 1
0 <= ranges[i] <= 100

```python

USER_FILENAME = "<user_code>"
import sys, json, builtins
import math, heapq, bisect, itertools, functools, collections, statistics, fractions, decimal, operator, array, random, re, string, os, pathlib
try:
    import resource as _res
except Exception:
    _res = None
from collections import Counter, defaultdict, deque, OrderedDict
from functools import lru_cache, reduce
from itertools import accumulate, permutations, combinations, product
from math import gcd, ceil, floor, sqrt
from decimal import Decimal
try:
    from typing import *
except Exception:
    pass
try:
    sys.setrecursionlimit(1_000_000)
except Exception:
    pass
try:
    import site as _site
    try:
        _sys_sites = _site.getsitepackages() if hasattr(_site, "getsitepackages") else []
        for _p in _sys_sites:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
    try:
        _usp = _site.getusersitepackages()
        if isinstance(_usp, str):
            _usp = [_usp]
        for _p in _usp:
            if _p and _p not in sys.path:
                sys.path.append(_p)
    except Exception:
        pass
except Exception:
    pass

def _disabled_input(*args, **kwargs):
    raise RuntimeError("input() is disabled in callable mode")
builtins.input = _disabled_input

ns = {"__name__": "__judge__"}  # prevent if __name__ == "__main__" blocks
for _k, _v in list(globals().items()):
    if not _k.startswith("_"):
        ns[_k] = _v
_CODE = "class Solution:\n    def minTaps(self, n: int, ranges: List[int]) -> int:\n#         taps=[]\n#         for i in range(len(ranges)):\n#             taps.append((i-ranges[i],i+ranges[i]))\n        \n#         taps.sort()\n#         @lru_cache(None)\n#         def helper(i):\n#             # minimum number of taps to open if we open i to reach end\n#             if i>=n+1:return float('inf')\n#             if taps[i][1]>=n:return 1\n#             ans=float('inf')\n#             # lets do binary search here\n#             start=i+1\n#             end=n\n#             lastindex=-1\n#             # get the last index which is smaller than taps[i][1]\n#             while start<=end:\n#                 mid=start+(end-start)//2\n#                 if taps[mid][0]<=taps[i][1]:\n#                     lastindex=mid\n#                     start=mid+1\n#                 else:\n#                     end=mid-1\n#             if lastindex==-1:return ans\n#             for j in range(i+1,lastindex+1):\n#                 if taps[j][0]>taps[i][1]:\n#                     break\n#                 if taps[j][0]<=taps[i][1] and taps[j][1]>taps[i][1]:\n#                     # benefit of picking this guy\n#                     ans=min(ans,1+helper(j))\n                    \n#             # sequential code to do that\n#             # dont go for binary unless interviewer say so\n#             # ask him in the approach if he wants to\n            \n#             # for j in range(i+1,n+1):\n#             #     if taps[j][0]>taps[i][1]:\n#             #         break\n#             #     if taps[j][0]<=taps[i][1] and taps[j][1]>taps[i][1]:\n#             #         # benefit of picking this guy\n#             #         ans=min(ans,1+helper(j))\n#             return ans\n#         ans=float('inf')\n#         for i in range(n,-1,-1):\n#             res=helper(i)\n#             if taps[i][0]<=0 and res<ans:\n#                 ans=res\n#         return -1 if ans==float('inf') else ans\n    \n        best = [float('inf') for _ in ranges]\n        for i, r in enumerate(ranges):\n            if r > 0:\n                start, end = i - r, i + r \n                best_with = 1 + (best[start] if start > 0 else 0)\n                for j in range(max(0, start), min(len(ranges), end+1)):\n                    best[j] = min(best[j], best_with)\n        if any(v for v in best if v == float('inf')):\n            return -1 \n        return best[-1]\n                \n        \n            \n        \n                    \n                    \n                    \n                \n            \n        \n"
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'minTaps'
if _fn_name:
    if "Solution" in ns:
        try:
            _obj = ns["Solution"]()
            if hasattr(_obj, _fn_name):
                _target = getattr(_obj, _fn_name)
        except Exception:
            _target = None
    if _target is None and _fn_name in ns and callable(ns[_fn_name]):
        _target = ns[_fn_name]
# Fallback: if there's exactly one user-defined function, use it
if _target is None:
    _cands = [v for k, v in ns.items() if callable(v) and getattr(v, "__module__", "") in ("__judge__", "__main__")]
    _user_funcs = [c for c in _cands if getattr(c, "__name__", "").startswith("_") is False]
    if len(_user_funcs) == 1:
        _target = _user_funcs[0]
if _target is None:
    raise RuntimeError(f"Could not resolve callable '{_fn_name}'")

_raw = sys.stdin.read().strip()
if _raw:
    _parsed = json.loads(_raw)
    if isinstance(_parsed, dict):
        _kwargs = _parsed.get("kwargs", {})
        _args = _parsed.get("args", [])
    else:
        _args, _kwargs = _parsed, {}
else:
    _args, _kwargs = [], {}
if not isinstance(_args, (list, tuple)):
    _args = [_args]
_res = _target(*_args, **_kwargs)
try:
    sys.stdout.write(repr(_res) + "\n")
except Exception:
    pass

```

Measured memory_bytes: 6200