<p>A <strong>ramp</strong> in an integer array <code>nums</code> is a pair <code>(i, j)</code> for which <code>i &lt; j</code> and <code>nums[i] &lt;= nums[j]</code>. The <strong>width</strong> of such a ramp is <code>j - i</code>.</p>

<p>Given an integer array <code>nums</code>, return <em>the maximum width of a <strong>ramp</strong> in </em><code>nums</code>. If there is no <strong>ramp</strong> in <code>nums</code>, return <code>0</code>.</p>

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

<pre>
<strong>Input:</strong> nums = [6,0,8,2,1,5]
<strong>Output:</strong> 4
<strong>Explanation:</strong> The maximum width ramp is achieved at (i, j) = (1, 5): nums[1] = 0 and nums[5] = 5.
</pre>

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

<pre>
<strong>Input:</strong> nums = [9,8,1,0,1,9,4,0,4,1]
<strong>Output:</strong> 7
<strong>Explanation:</strong> The maximum width ramp is achieved at (i, j) = (2, 9): nums[2] = 1 and nums[9] = 1.
</pre>

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

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

class Solution:
    def maxWidthRamp(self, nums: List[int]) -> int:
        n = len(nums)
        ans = 0

        minValSoFar = [(0, nums[0])]
        for index in range(0, n):
            if nums[index] < minValSoFar[-1][1]:
                minValSoFar.append((index, nums[index]))

        maxValSoFar = [(n - 1, nums[n - 1])]
        for index in range(n - 1, -1, -1):
            if nums[index] > maxValSoFar[-1][1]:
                maxValSoFar.append((index, nums[index]))
        maxValSoFar = maxValSoFar

        if maxValSoFar[-1][1] < minValSoFar[0][1]:
            return 0

        i, j = 0, len(maxValSoFar) - 1

        while i < len(minValSoFar) and j >= 0:
            
            indexLeft, valLeft = minValSoFar[i]
            indexRight, valRight = maxValSoFar[j]

            if valRight >= valLeft:
                ans = max(ans, indexRight - indexLeft)
                j -= 1 
            else:
                i += 1 

        return ans

        
26000