<p>Given a <strong>0-indexed</strong> integer array <code>nums</code> of size <code>n</code> and two integers <code>lower</code> and <code>upper</code>, return <em>the number of fair pairs</em>.</p>

<p>A pair <code>(i, j)</code> is <b>fair </b>if:</p>

<ul>
	<li><code>0 &lt;= i &lt; j &lt; n</code>, and</li>
	<li><code>lower &lt;= nums[i] + nums[j] &lt;= upper</code></li>
</ul>

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

<pre>
<strong>Input:</strong> nums = [0,1,7,4,4,5], lower = 3, upper = 6
<strong>Output:</strong> 6
<strong>Explanation:</strong> There are 6 fair pairs: (0,3), (0,4), (0,5), (1,3), (1,4), and (1,5).
</pre>

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

<pre>
<strong>Input:</strong> nums = [1,7,9,2,5], lower = 11, upper = 11
<strong>Output:</strong> 1
<strong>Explanation:</strong> There is a single fair pair: (2,3).
</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>nums.length == n</code></li>
	<li><code><font face="monospace">-10<sup>9</sup></font>&nbsp;&lt;= nums[i] &lt;= 10<sup>9</sup></code></li>
	<li><code><font face="monospace">-10<sup>9</sup>&nbsp;&lt;= lower &lt;= upper &lt;= 10<sup>9</sup></font></code></li>
</ul>

class Solution:
    def countFairPairs(self, nums: List[int], lower: int, upper: int) -> int:
        nums.sort()
        #print(nums)
        leftbound = len(nums) - 1
        rightbound = len(nums) - 1
        pairs = 0
        for i in range(len(nums) - 1):
            if nums[i] + nums[rightbound] < lower:
                continue
            left = i + 1
            right = max(i+1, leftbound)
            while left < right:
                mid = left + (right - left) // 2
                if nums[mid] + nums[i] < lower:
                    left = mid + 1
                else:
                    right = mid

            leftbound = right 

            left = leftbound 
            right = rightbound
            if left > right:
                break
            while left <= right:
                mid = left + (right - left) // 2
                if nums[mid] + nums[i] > upper:
                    right = mid - 1
                else:
                    left = mid + 1
            
            rightbound = right

            pairs += rightbound - leftbound + 1
            #print(leftbound, rightbound, pairs)

        return pairs


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