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"title": "Count the Number of Incremovable Subarrays II",
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"content": "<p>You are given a <strong>0-indexed</strong> array of <strong>positive</strong> integers <code>nums</code>.</p>\n\n<p>A subarray of <code>nums</code> is called <strong>incremovable</strong> if <code>nums</code> becomes <strong>strictly increasing</strong> on removing the subarray. For example, the subarray <code>[3, 4]</code> is an incremovable subarray of <code>[5, 3, 4, 6, 7]</code> because removing this subarray changes the array <code>[5, 3, 4, 6, 7]</code> to <code>[5, 6, 7]</code> which is strictly increasing.</p>\n\n<p>Return <em>the total number of <strong>incremovable</strong> subarrays of</em> <code>nums</code>.</p>\n\n<p><strong>Note</strong> that an empty array is considered strictly increasing.</p>\n\n<p>A <strong>subarray</strong> is a contiguous non-empty sequence of elements within an array.</p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [1,2,3,4]\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> The 10 incremovable subarrays are: [1], [2], [3], [4], [1,2], [2,3], [3,4], [1,2,3], [2,3,4], and [1,2,3,4], because on removing any one of these subarrays nums becomes strictly increasing. Note that you cannot select an empty subarray.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [6,5,7,8]\n<strong>Output:</strong> 7\n<strong>Explanation:</strong> The 7 incremovable subarrays are: [5], [6], [5,7], [6,5], [5,7,8], [6,5,7] and [6,5,7,8].\nIt can be shown that there are only 7 incremovable subarrays in nums.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [8,7,6,6]\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> The 3 incremovable subarrays are: [8,7,6], [7,6,6], and [8,7,6,6]. Note that [8,7] is not an incremovable subarray because after removing [8,7] nums becomes [6,6], which is sorted in ascending order but not strictly increasing.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n</ul>\n",
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"Calculate the largest <code>x</code> such that <code>nums[0..x]</code> is strictly increasing.",
"Calculate the smallest <code>y</code> such that <code>nums[y..nums.length-1]</code> is strictly increasing.",
"For each <code>i</code> in <code>[0, x]</code>, select the smallest <code>j</code> in <code>[y, nums.length - 1]</code>. Then we can keep the prefix with any suffix of <code>[j, nums.length - 1]</code> (including the empty one).",
"Note that when <code>i</code> increases, <code>j</code> wont decrease. Use two-pointers.",
"Note that we cannot delete an empty array, but we can delete the whole array."
],
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