Grid Sum Quest

Given a 4x4 grid of integers, find the number of unique paths starting from the top-left (0,0) and ending at the bottom-right (3,3) such that the sum of all numbers visited on the path is exactly S. You can move Up, Down, Left, or Right. You cannot visit the same cell twice in a single path. Input: The first line is the target sum S. The next 4 lines contain 4 integers each representing the grid. Example: Input: 10 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 Output: 0 (Explanation: The shortest path is 7 cells long, minimum sum is 7. No path of sum 10 exists from (0,0) to (3,3) in this grid.)