<p>Given an array of integers <code>nums</code> and an integer <code>limit</code>, return the size of the longest <strong>non-empty</strong> subarray such that the absolute difference between any two elements of this subarray is less than or equal to <code>limit</code><em>.</em></p>

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

<pre>
<strong>Input:</strong> nums = [8,2,4,7], limit = 4
<strong>Output:</strong> 2 
<strong>Explanation:</strong> All subarrays are: 
[8] with maximum absolute diff |8-8| = 0 &lt;= 4.
[8,2] with maximum absolute diff |8-2| = 6 &gt; 4. 
[8,2,4] with maximum absolute diff |8-2| = 6 &gt; 4.
[8,2,4,7] with maximum absolute diff |8-2| = 6 &gt; 4.
[2] with maximum absolute diff |2-2| = 0 &lt;= 4.
[2,4] with maximum absolute diff |2-4| = 2 &lt;= 4.
[2,4,7] with maximum absolute diff |2-7| = 5 &gt; 4.
[4] with maximum absolute diff |4-4| = 0 &lt;= 4.
[4,7] with maximum absolute diff |4-7| = 3 &lt;= 4.
[7] with maximum absolute diff |7-7| = 0 &lt;= 4. 
Therefore, the size of the longest subarray is 2.
</pre>

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

<pre>
<strong>Input:</strong> nums = [10,1,2,4,7,2], limit = 5
<strong>Output:</strong> 4 
<strong>Explanation:</strong> The subarray [2,4,7,2] is the longest since the maximum absolute diff is |2-7| = 5 &lt;= 5.
</pre>

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

<pre>
<strong>Input:</strong> nums = [4,2,2,2,4,4,2,2], limit = 0
<strong>Output:</strong> 3
</pre>

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

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code>0 &lt;= limit &lt;= 10<sup>9</sup></code></li>
</ul>

'''
[10,1,2,4,7,2]
Brute Force
n + (n-1) + n-2 + + + == O(n^2)
mono deques
limit = 4
  0 1 2 3 4 5
[10,1,2,4,7,2]
    ^
10, 0
 1, 1

10 
10

'''
class Solution:
    def longestSubarray(self, nums: List[int], limit: int) -> int:
        inc_mins, dec_maxs = deque(), deque()
        l, res = 0, 0
        for r, n in enumerate(nums):
            while len(dec_maxs) > 0 and nums[dec_maxs[-1]] < n:
                dec_maxs.pop()
            dec_maxs.append(r)

            while len(inc_mins) > 0 and nums[inc_mins[-1]] > n:
                inc_mins.pop()
            inc_mins.append(r)


            while inc_mins and dec_maxs and abs(nums[inc_mins[0]] - nums[dec_maxs[0]]) > limit:
                if l == inc_mins[0]:
                    inc_mins.popleft()
                if l == dec_maxs[0]:
                    dec_maxs.popleft()
                l += 1
            res = max(res, r - l + 1)
        return res


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