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 = '# 1326. Minimum Number of Taps to Open to Water a Garden\n\ndef redundant (a, b):\n    (al, ar), (bl, br) = a, b\n    return al <= bl <= br <= ar or bl <= al <= ar <= br\n\ndef union (a, b):\n    (al, ar), (bl, br) = a, b\n    return (min (al, bl), max (ar, br))\n\ndef remove_overlap (ranges):\n    ans = []\n    for rng in ranges:\n        ans.append (rng)\n        while len (ans) >= 2 and redundant (ans[-2], ans[-1]):\n            b = ans.pop (); a = ans.pop ()\n            ans.append (union (a, b))\n    return ans\n\ndef union_covers (a, b, c):\n    (al, ar), (bl, br), (cl, cr) = a, b, c\n    return al <= cl <= ar <= cr and al <= bl <= br <= cr\n\ndef min_taps (n, radii):\n    assert n >= 1\n    assert len (radii) == n + 1\n    \n    ranges = []\n    for (center, radius) in enumerate (radii):\n        if radius > 0:\n            left_end = max (0, center - radius)\n            right_end = min (n, center + radius)\n            ranges.append ((left_end, right_end))\n\n    ranges = remove_overlap (ranges)\n\n    final_ranges = []\n    for rng in ranges:\n        if len (final_ranges) >= 2 and union_covers (final_ranges[-2], final_ranges[-1], rng):\n            final_ranges.pop ()\n        final_ranges.append (rng)\n\n    if final_ranges and final_ranges[0][0] == 0 and final_ranges[-1][-1] == n and all (final_ranges[i][1] >= final_ranges[i+1][0] for i in range (len (final_ranges) - 1)):\n        return len (final_ranges)\n    else:\n        return -1\n\n\nclass Solution:\n    def minTaps(self, n: int, ranges: List[int]) -> int:\n        return min_taps(n, ranges)'
_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: 7496