<p>You have a <code>grid</code> of size <code>n x 3</code> and you want to paint each cell of the grid with exactly one of the three colors: <strong>Red</strong>, <strong>Yellow,</strong> or <strong>Green</strong> while making sure that no two adjacent cells have the same color (i.e., no two cells that share vertical or horizontal sides have the same color).</p>

<p>Given <code>n</code> the number of rows of the grid, return <em>the number of ways</em> you can paint this <code>grid</code>. As the answer may grow large, the answer <strong>must be</strong> computed modulo <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2020/03/26/e1.png" style="width: 400px; height: 257px;" />
<pre>
<strong>Input:</strong> n = 1
<strong>Output:</strong> 12
<strong>Explanation:</strong> There are 12 possible way to paint the grid as shown.
</pre>

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

<pre>
<strong>Input:</strong> n = 5000
<strong>Output:</strong> 30228214
</pre>

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

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

static const int mod = 1e9+7;
class Solution {
public:
    int numOfWays(int n) {
        map<string,unsigned long long> prev{{"RGR",1},{"RGY",1},{"RYR",1},{"RYG",1},
                                {"GRG",1},{"GRY",1},{"GYR",1},{"GYG",1},
                                {"YRG",1},{"YRY",1},{"YGR",1},{"YGY",1}};
        unordered_map<string,vector<string>> stepMap{{"GRG" , {"RGR","RGY" , "RYR" , "YGR" ,"YGY"}},
                                          {"GRY" , {"RGR","RYR" , "RYG" , "YGR" } },
                                          {"GYG" , {"RGR","RGY" , "YRY" , "YGR" ,"YGY"} },
                                          {"GYR" , {"RGY","YRG" , "YRY" , "YGY" } },
                                          {"RGR" , {"GRG","GRY" , "GYG" , "YRG" ,"YRY"} },
                                          {"RGY" , {"GRG","GYR" , "GYG" , "YRG" } },
                                          {"RYG" , {"GRY","YRY" , "YGR" , "YGY" } },
                                          {"RYR" , {"GRG","GRY" , "YRG" , "YRY" ,"YGY"}},
                                          {"YGR" , {"RYG","GRG" , "GRY" , "GYG" }},
                                          {"YGY" , {"RYR","RYG" , "GRG" , "GYR" ,"GYG"}},
                                          {"YRG" , {"RGR","RGY" , "RYR" , "GYR" }},
                                          {"YRY" , {"RGR","RYR" , "RYG" , "GYR" ,"GYG"}}};
        auto cur = prev;
        cur.clear();
        for(int i = 2;i <=n;++i){
            for(const auto& item:prev){
                string key = item.first;
                for(auto& next: stepMap[key]){
                    cur[next] += item.second;
                    cur[next] %= mod;
                }
            }
            prev = cur;
            cur.clear();
        }
        unsigned long long ret = 0;
        for(auto& item:prev){
            ret += item.second;
        }
        return ret%mod;
    }
};
65525