Simple 3D dp Solution
Code
# Code
```cpp
int mod = 1000000007;

//memoization soln
int helper(int i, int j, int mask, int &m, int &n, vector<vector<vector<int>>> &dp){ //mask:[0, i) stores mask for curr col, rest for prev col
    if (i == n){ return 1; }

    if (dp[i][j][mask] == -1){ //compute if not already
        int count = 0;
        int curr0 = j*2, curr1 = j*2 + 1, prev0 = j*2 - 2, prev1 = j*2 - 1;

        if (j == m){ count = helper(i + 1, 0, mask, m, n, dp); }
        else {
            if ((mask&(1<<curr0)) > 0 || (mask&(1<<curr1)) == 0){ //red 
                if (j == 0 || (mask&(1<<prev0)) > 0 || (mask&(1<<prev1)) == 0){
                    count = (count + helper(i, j + 1, (mask&(~(1<<curr0)))|(1<<curr1), m, n, dp))%mod;
                }
            }
            if ((mask&(1<<curr0)) == 0 || (mask&(1<<curr1)) > 0){ //green 
                if (j == 0 || (mask&(1<<prev0)) == 0 || (mask&(1<<prev1)) > 0){
                    count = (count + helper(i, j + 1, (mask|(1<<curr0))&(~(1<<curr1)), m, n, dp))%mod;
                }
            }
            if ((mask&(1<<curr0)) == 0 || (mask&(1<<curr1)) == 0){ //blue
                if (j == 0 || (mask&(1<<prev0)) == 0 || (mask&(1<<prev1)) == 0){
                    count = (count + helper(i, j + 1, (mask|(1<<curr0))|(1<<curr1), m, n, dp))%mod;
                }
            }
        }

        dp[i][j][mask] = count;
    }

    return dp[i][j][mask];
}

int colorTheGrid(int m, int n){ 
    vector<vector<vector<int>>> dp(n + 1, vector<vector<int>>(m + 1, vector<int>(pow(2, 2*m), -1))); //3D dp array
    return helper(0, 0, 0, m, n, dp); 
}
//tabulation yumpossible due to j = 0 prolly
```
['Dynamic Programming', 'Bit Manipulation', 'Bitmask', 'C++']