Build a Matrix With Conditions

You are given a **positive** integer `k`. You are also given: - a 2D integer array `rowConditions` of size `n` where `rowConditions[i] = [abovei, belowi]`, and - a 2D integer array `colConditions` of size `m` where `colConditions[i] = [lefti, righti]`. The two arrays contain integers from `1` to `k`. You have to build a `k x k` matrix that contains each of the numbers from `1` to `k` **exactly once**. The remaining cells should have the value `0`. The matrix should also satisfy the following conditions: - The number `abovei` should appear in a **row** that is strictly **above** the row at which the number `belowi` appears for all `i` from `0` to `n - 1`. - The number `lefti` should appear in a **column** that is strictly **left** of the column at which the number `righti` appears for all `i` from `0` to `m - 1`. Return _**any** matrix that satisfies the conditions_. If no answer exists, return an empty matrix.   **Example 1:** **Input:** k = 3, rowConditions = [[1,2],[3,2]], colConditions = [[2,1],[3,2]] **Output:** [[3,0,0],[0,0,1],[0,2,0]] **Explanation:** The diagram above shows a valid example of a matrix that satisfies all the conditions. The row conditions are the following: - Number 1 is in row 1, and number 2 is in row 2, so 1 is above 2 in the matrix. - Number 3 is in row 0, and number 2 is in row 2, so 3 is above 2 in the matrix. The column conditions are the following: - Number 2 is in column 1, and number 1 is in column 2, so 2 is left of 1 in the matrix. - Number 3 is in column 0, and number 2 is in column 1, so 3 is left of 2 in the matrix. Note that there may be multiple correct answers. ``` **Example 2:** **Input:** k = 3, rowConditions = [[1,2],[2,3],[3,1],[2,3]], colConditions = [[2,1]] **Output:** [] **Explanation:** From the first two conditions, 3 has to be below 1 but the third conditions needs 3 to be above 1 to be satisfied. No matrix can satisfy all the conditions, so we return the empty matrix. ```   **Constraints:** - `2 <= k <= 400` - `1 <= rowConditions.length, colConditions.length <= 104` - `rowConditions[i].length == colConditions[i].length == 2` - `1 <= abovei, belowi, lefti, righti <= k` - `abovei != belowi` - `lefti != righti`