There is an $m imes n$ grid where a robot starts at the coordinates startPos $= [ ext{start}_{ ext{row}}, ext{start}_{ ext{col}}]$ and aims to travel to its destination at homePos $= [ ext{home}_{ ext{row}}, ext{home}_{ ext{col}}]$.

At each step, the robot can move one cell up, down, left, or right. The cost of each movement depends only on the target cell:

• Moving into any cell in row $r$ costs rowCosts[r].

• Moving into any cell in column $c$ costs colCosts[c].

The robot does not pay any cost for its starting cell.

Return the minimum total cost for the robot to move from startPos to homePos.

Constraints:

• m $==$ rowCosts.length

• n $==$ colCosts.length

• $1 \leq m, n \leq 10^5$

• $0 \leq$ rowCosts[r], colCosts[c] $\leq 10^4$

• startPos.length $== 2$

• homePos.length $== 2$

• $0 \leq ext{start}_{ ext{row}}, ext{home}_{ ext{row}} < m$

• $0 \leq ext{start}_{ ext{col}}, ext{home}_{ ext{col}} < n$

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