<p>The chess knight has a <strong>unique movement</strong>,&nbsp;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 diagram:</p>

<p>A chess knight can move as indicated in the chess diagram below:</p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/chess.jpg" style="width: 402px; height: 402px;" />
<p>We have a chess knight and a phone pad as shown below, the knight <strong>can only stand on a numeric cell</strong>&nbsp;(i.e. blue cell).</p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/08/18/phone.jpg" style="width: 242px; height: 322px;" />
<p>Given an integer <code>n</code>, return how many distinct phone numbers of length <code>n</code> we can dial.</p>

<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>

<p>As the answer may be very large, <strong>return the answer modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

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

<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 10
<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.
</pre>

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

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 20
<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]
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> n = 3131
<strong>Output:</strong> 136006598
<strong>Explanation:</strong> Please take care of the mod.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 5000</code></li>
</ul>

class Solution {
public:
    int knightDialer(int n) {
        constexpr int kMod = 1'000'000'007;
        const vector<pair<int, int>> dirs = {{-2, 1},  {-1, 2}, {1, 2},
                                             {2, 1},   {2, -1}, {1, -2},
                                             {-1, -2}, {-2, -1}};
        vector<vector<int>> dp(4, vector<int>(3, 1));
        dp[3][0] = dp[3][2] = 0;

        for (int k = 0; k < n - 1; ++k) {
            vector<vector<int>> newDp(4, vector<int>(3));
            for (int i = 0; i < 4; ++i)
                for (int j = 0; j < 3; ++j) {
                    if (isNotNumericCell(i, j))
                        continue;
                    for (const auto& [dx, dy] : dirs) {
                        const int x = i + dx;
                        const int y = j + dy;
                        if (x < 0 || x >= 4 || y < 0 || y >= 3)
                            continue;
                        if (isNotNumericCell(x, y))
                            continue;
                        newDp[i][j] = (newDp[i][j] + dp[x][y]) % kMod;
                    }
                }
            dp = move(newDp);
        }

        int ans = 0;

        for (const vector<int>& row : dp)
            for (const int a : row)
                ans = (ans + a) % kMod;

        return ans;
    }

private:
    bool isNotNumericCell(int i, int j) { return i == 3 && (j == 0 || j == 2); }
};
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