<p>You are given an integer array <code>arr</code>. From some starting index, you can make a series of jumps. The (1<sup>st</sup>, 3<sup>rd</sup>, 5<sup>th</sup>, ...) jumps in the series are called <strong>odd-numbered jumps</strong>, and the (2<sup>nd</sup>, 4<sup>th</sup>, 6<sup>th</sup>, ...) jumps in the series are called <strong>even-numbered jumps</strong>. Note that the <strong>jumps</strong> are numbered, not the indices.</p>

<p>You may jump forward from index <code>i</code> to index <code>j</code> (with <code>i &lt; j</code>) in the following way:</p>

<ul>
	<li>During <strong>odd-numbered jumps</strong> (i.e., jumps 1, 3, 5, ...), you jump to the index <code>j</code> such that <code>arr[i] &lt;= arr[j]</code> and <code>arr[j]</code> is the smallest possible value. If there are multiple such indices <code>j</code>, you can only jump to the <strong>smallest</strong> such index <code>j</code>.</li>
	<li>During <strong>even-numbered jumps</strong> (i.e., jumps 2, 4, 6, ...), you jump to the index <code>j</code> such that <code>arr[i] &gt;= arr[j]</code> and <code>arr[j]</code> is the largest possible value. If there are multiple such indices <code>j</code>, you can only jump to the <strong>smallest</strong> such index <code>j</code>.</li>
	<li>It may be the case that for some index <code>i</code>, there are no legal jumps.</li>
</ul>

<p>A starting index is <strong>good</strong> if, starting from that index, you can reach the end of the array (index <code>arr.length - 1</code>) by jumping some number of times (possibly 0 or more than once).</p>

<p>Return <em>the number of <strong>good</strong> starting indices</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> arr = [10,13,12,14,15]
<strong>Output:</strong> 2
<strong>Explanation:</strong> 
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.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> arr = [2,3,1,1,4]
<strong>Output:</strong> 3
<strong>Explanation:</strong> 
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 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 (even-numbered), 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 (odd-numbered), 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&#39;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&#39;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.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> arr = [5,1,3,4,2]
<strong>Output:</strong> 3
<strong>Explanation:</strong> We can reach the end from starting indices 1, 2, and 4.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= arr.length &lt;= 2 * 10<sup>4</sup></code></li>
	<li><code>0 &lt;= arr[i] &lt; 10<sup>5</sup></code></li>
</ul>

class Solution:
    def oddEvenJumps(self, arr: List[int]) -> int:
        if len(arr)==1:
            return 1
        A = [[arr[i],i] for i in range(len(arr))]
        sorted_arr = sorted(A)
        greater = self.greaterOrEqualOnRight(sorted_arr)
        smaller = self.smallerOrEqualOnRight(arr)
        odd = [False for i in range(len(arr))]
        even = [False for i in range(len(arr))]
        ans = 0
        for i in range(len(arr)-2, -1, -1):
            index = greater[i]
            if index == len(arr)-1:
                odd[i] = True
            elif index == -1:
                odd[i] = False
            else:
                odd[i] = even[index]
                
            
            index  = smaller[i]
            if index == len(arr)-1:
                even[i] = True
            elif index == -1:
                even[i] = False
            else:
                even[i] = odd[index]
            
            if odd[i] == True:
                ans+=1
        odd[len(arr)-1] = True
        even[len(arr)-1] = True
        ans +=1
        # for i in range(len(arr)):
        #     if odd[i] == True:
        #         ans+=1
        return ans
        
    def greaterOrEqualOnRight(self, arr):
        stack = []
        ans = [-1 for i in range(len(arr))]
        for element, index in arr:
            if len(stack) == 0:
                stack.append(index)
            else:
                while len(stack) > 0 and stack[-1] < index:
                    ans[stack.pop()] = index
                stack.append(index)
        return ans

    def smallerOrEqualOnRight(self, arr):
        A = [[-1*arr[i],i] for i in range(len(arr))]
        sorted_arr = sorted(A)
        return self.greaterOrEqualOnRight(sorted_arr)

# [1,2,3,2,1,4,4,5]

# 1->1->4->4->5
# 2->3->1->4->4->5
# 3->4->4->5
# 2->4->4->5
# 1->4->4->5
# 4->4->[not possible]
# 4->5
# 5
            
        # while stack
        # stack = [1]
        # ans = [1,4,3,4,-1]
        # while 
# odd -> smallest greater or equal value
# even-> largest smaller or equal value

#     [2,3,1,1,4]

# odd [(true)   (true)  (false)    (true)  (true)]
# even [(false)   (false)   (true) (false) (true)]

# smallest greater or equal index
# smalest smaller or equal index

# [2, 3, 1, 1, 4]
            
#   [(2,0) -> (3, 1)]  
#   [(1,2) -> (1, 3)]
# [(1,3)->(4,4)]
# [(4,4) -> (4,4)]
# [(3,1) -> (4,4)]
    
#     [3,4]
# [1,2,3,2,1,4,4,5]
# # [[1, 0], [1, 4], [2, 1], [2, 3], [3, 2], [4, 5], [4, 6], [5, 7]]
# # [[-5,7], [-4,5], [-4,6], [-3,2], [-2,1], [-2,3], [-1,0], [-1,4]]

# 0->4
# 1->3
# 2->5
# 5->6
# 3->5
# 4->5
# 5->6
# 6->7
# [7]


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