<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:
        n = len(nums)
        count = 0
        nums.sort()
        
        def search(target: int, low: int, high: int) -> int:
            if low > high:
                return low
            mid = (low + high) // 2
            if nums[mid] > target:
                return search(target, low, mid - 1)
            else:
                return search(target, mid + 1, high)
        for i, x in enumerate(nums):
            l = lower - x
            u = upper - x
            low = search(l - 1, i + 1, n - 1)
            high = search(u, i + 1, n - 1)
            count += max(0, high - low)
        return count
1719