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"title": "Knight Dialer",
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"content": "<p>The chess knight has a <strong>unique movement</strong>, it may move two squares vertically and one square horizontally, or two squares horizontally and one square vertically (with both forming the shape of an <strong>L</strong>). The possible movements of chess knight are shown in this diagaram:</p>\n\n<p>A chess knight can move as indicated in the chess diagram below:</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/18/chess.jpg\" style=\"width: 402px; height: 402px;\" />\n<p>We have a chess knight and a phone pad as shown below, the knight <strong>can only stand on a numeric cell</strong> (i.e. blue cell).</p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/08/18/phone.jpg\" style=\"width: 242px; height: 322px;\" />\n<p>Given an integer <code>n</code>, return how many distinct phone numbers of length <code>n</code> we can dial.</p>\n\n<p>You are allowed to place the knight <strong>on any numeric cell</strong> initially and then you should perform <code>n - 1</code> jumps to dial a number of length <code>n</code>. All jumps should be <strong>valid</strong> knight jumps.</p>\n\n<p>As the answer may be very large, <strong>return the answer modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>\n\n<p> </p>\n<p><strong>Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 1\n<strong>Output:</strong> 10\n<strong>Explanation:</strong> We need to dial a number of length 1, so placing the knight over any numeric cell of the 10 cells is sufficient.\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 2\n<strong>Output:</strong> 20\n<strong>Explanation:</strong> All the valid number we can dial are [04, 06, 16, 18, 27, 29, 34, 38, 40, 43, 49, 60, 61, 67, 72, 76, 81, 83, 92, 94]\n</pre>\n\n<p><strong>Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> n = 3131\n<strong>Output:</strong> 136006598\n<strong>Explanation:</strong> Please take care of the mod.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= n <= 5000</code></li>\n</ul>\n",
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