Count the Number of Fair Pairs
<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>
Array; Two Pointers; Binary Search; Sorting
function countFairPairs(nums: number[], lower: number, upper: number): number {
    const search = (x: number, l: number): number => {
        let r = nums.length;
        while (l < r) {
            const mid = (l + r) >> 1;
            if (nums[mid] >= x) {
                r = mid;
            } else {
                l = mid + 1;
            }
        }
        return l;
    };

    nums.sort((a, b) => a - b);
    let ans = 0;
    for (let i = 0; i < nums.length; ++i) {
        const j = search(lower - nums[i], i + 1);
        const k = search(upper - nums[i] + 1, i + 1);
        ans += k - j;
    }
    return ans;
}
