You are given an integer array
arr. From some starting index, you can make a series of jumps. The (1^{st}, 3^{rd}, 5^{th}, ...) jumps in the series are called oddnumbered jumps, and the (2^{nd}, 4^{th}, 6^{th}, ...) jumps in the series are called evennumbered jumps. Note that the jumps are numbered, not the indices.
You may jump forward from index i
to index j
(with i < j
) in the following way:
 During oddnumbered jumps (i.e., jumps 1, 3, 5, ...), you jump to the index
j
such thatarr[i] <= arr[j]
andarr[j]
is the smallest possible value. If there are multiple such indicesj
, you can only jump to the smallest such indexj
.  During evennumbered jumps (i.e., jumps 2, 4, 6, ...), you jump to the index
j
such that arr[i] >= arr[j]
andarr[j]
is the largest possible value. If there are multiple such indicesj
, you can only jump to the smallest such indexj
.  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 arr.length  1
) by jumping some number of times (possibly 0 or more than once).
Return the number of good starting indices.
Example 1:
Input: arr = [10,13,12,14,15]
Output: 2
Explanation:
From starting index i = 0, we can make our 1st jump to i = 2
(since arr[2] is the smallest among arr[1], arr[2], arr[3], arr[4]
that is greater or equal to arr[0]), then we cannot jump any more.
From starting index i = 1 and i = 2, we can make our 1st jump to i = 3,
then we cannot jump any more.
From starting index i = 3, we can make our 1st jump to i = 4,
so we have reached the end.
From starting index i = 4, we have reached the end already.
In total, there are 2 different starting indices i = 3 and i = 4,
where we can reach the end with some number of jumps.
Example 2:
Input: arr = [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 (oddnumbered), we first jump to i = 1 because arr[1] is the
smallest value in [arr[1], arr[2], arr[3], arr[4]] that is greater than or
equal to arr[0].
During our 2nd jump (evennumbered), we jump from i = 1 to i = 2 because arr[2]
is the largest value in [arr[2], arr[3], arr[4]] that is less than or equal
to arr[1]. arr[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 (oddnumbered), we jump from i = 2 to i = 3 because arr[3] is
the smallest value in [arr[3], arr[4]] that is greater than or equal to arr[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 indices i = 1, i = 3, and i = 4,
where we can reach the end with some number of jumps.
Example 3:
Input: arr = [5,1,3,4,2]
Output: 3
Explanation: We can reach the end from starting indices 1, 2, and 4.
Constraints:
1 <= arr.length <= 2 * 10^{4}
0 <= arr[i] < 10^{5}

