<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>

from collections import deque
class Solution:
    def maxWidthRamp(self, nums: List[int]) -> int:
        a = deque([])
        # populate the decreasing decreasing ramp (begin of ramp)
        for idx, num in enumerate(nums):
            if len(a) == 0:
                a.append((idx, num))
            else:
                if num < a[-1][1]:
                    a.append((idx, num))

        result = 0
        for re_idx in range(len(nums)):
            idx = len(nums) - 1 - re_idx
            num = nums[idx]
            while True:
                if len(a) == 0:
                    result = max(result, idx)
                    break
                if num < a[-1][1]:
                    break
                else:
                    result = max(result, idx - a[-1][0])
                    a.pop()
        return result
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