You are given an integer array A.  From some starting index, you can make a series of jumps.  The (1st, 3rd, 5th, ...) jumps in the series are called odd numbered jumps, and the (2nd, 4th, 6th, ...) jumps in the series are called even numbered jumps.
You may from index i jump forward to index j (with i < j) in the following way:

During odd numbered jumps (ie. jumps 1, 3, 5, ...), you jump to the index j such that A[i] <= A[j] and A[j] is the smallest possible value.  If there are multiple such indexes j, you can only jump to the smallest such index j.
During even numbered jumps (ie. jumps 2, 4, 6, ...), you jump to the index j such that A[i] >= A[j] and A[j] is the largest possible value.  If there are multiple such indexes j, you can only jump to the smallest such index j.
(It may be the case that for some index i, there are no legal jumps.)

A starting index is good if, starting from that index, you can reach the end of the array (index A.length - 1) by jumping some number of times (possibly 0 or more than once.)
Return the number of good starting indexes.
 
Example 1:
Input: [10,13,12,14,15]
Output: 2
Explanation: 
From starting index i = 0, we can jump to i = 2 (since A[2] is the smallest among A[1], A[2], A[3], A[4] that is greater or equal to A[0]), then we can't jump any more.
From starting index i = 1 and i = 2, we can jump to i = 3, then we can't jump any more.
From starting index i = 3, we can jump to i = 4, so we've reached the end.
From starting index i = 4, we've reached the end already.
In total, there are 2 different starting indexes (i = 3, i = 4) where we can reach the end with some number of jumps.


Example 2:
Input: [2,3,1,1,4]
Output: 3
Explanation: 
From starting index i = 0, we make jumps to i = 1, i = 2, i = 3:

During our 1st jump (odd numbered), we first jump to i = 1 because A[1] is the smallest value in (A[1], A[2], A[3], A[4]) that is greater than or equal to A[0].

During our 2nd jump (even numbered), we jump from i = 1 to i = 2 because A[2] is the largest value in (A[2], A[3], A[4]) that is less than or equal to A[1].  A[3] is also the largest value, but 2 is a smaller index, so we can only jump to i = 2 and not i = 3.

During our 3rd jump (odd numbered), we jump from i = 2 to i = 3 because A[3] is the smallest value in (A[3], A[4]) that is greater than or equal to A[2].

We can't jump from i = 3 to i = 4, so the starting index i = 0 is not good.

In a similar manner, we can deduce that:
From starting index i = 1, we jump to i = 4, so we reach the end.
From starting index i = 2, we jump to i = 3, and then we can't jump anymore.
From starting index i = 3, we jump to i = 4, so we reach the end.
From starting index i = 4, we are already at the end.
In total, there are 3 different starting indexes (i = 1, i = 3, i = 4) where we can reach the end with some number of jumps.


Example 3:
Input: [5,1,3,4,2]
Output: 3
Explanation: 
We can reach the end from starting indexes 1, 2, and 4.



 
Note:

1 <= A.length <= 20000
0 <= A[i] < 100000

```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 oddEvenJumps(self, A: List[int]) -> int:\n        odd_jump = {}\n        even_jump = {}\n        index_ele = {index: ele for index, ele in enumerate(A)}\n        # {0: 10. 2: 12, 1: 13}\n        sorted_A = sorted(list(range(len(A))), key=lambda x: A[x])\n        even_sorted_A = sorted(list(range(len(A))), key=lambda x: (A[x], -x))\n        # cache = {}\n        # sorted(index_ele.items(), key=lambda kv: (kv[1], kv[0]))\n        # print(sorted_A)\n        # [1: 3, 1:2, 2:0, 3:1, 4:4]\n        # [4: 4, 3: 1, 2:0. 1:2, 1:3]\n        # [4, 1, 0, 3]\n        stack = []\n        # [1, 1, 2,3,4]\n        for i in range(len(A)):\n            idx = sorted_A[i]\n            # idx = ele_index[ele]\n            while stack and stack[-1] < idx:\n                old_index = stack.pop()\n                odd_jump[old_index] = idx\n            stack.append(idx)\n        for idx in stack:\n            odd_jump[idx] = -1        \n        stack = []\n        for i in range(len(A) - 1, -1, -1):\n            idx = even_sorted_A[i]\n            # idx = ele_index[ele]\n            while stack and stack[-1] < idx:\n                old_index = stack.pop()\n                even_jump[old_index] = idx\n            stack.append(idx)\n        for idx in stack:\n            even_jump[idx] = -1\n        self.ans = 0\n        # print(odd_jump, even_jump)\n        @lru_cache(None)\n        def helper(index, odd):\n            if index == len(A) - 1:\n                # self.ans += 1\n                return 1\n            ans = 0\n            if index == -1:\n                return 0\n            # if (index, odd) in self.cache: return self.cache[(index, odd)]\n            if odd:\n                # print(index)\n                ans += helper(odd_jump[index], not odd)\n            else:\n                ans += helper(even_jump[index], not odd)\n                # [10, 12, 13, 14, 15]\n                # [0,   2,  1,  3,  4]\n                # 1\n                # 2   3   3  4 -1\n                # [15, 14, 13, 12, 10]\n                # [15, 14, 12, 10]\n                #  -1        13: 2\n            return ans\n        ans = 0\n        for i in range(len(A)):\n            ans += helper(i, True)\n        return ans\n'
_co = compile(_CODE, USER_FILENAME, "exec")
exec(_co, ns, ns)

_target = None
_fn_name = 'oddEvenJumps'
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: 10386