Permutation Paths in Grid

Given an n x n grid filled with unique integers from 1 to n^2, you need to find all unique permutations of numbers starting from the top-left corner (1,1) to the bottom-right corner (n,n). A valid move can either be to the right or down. Print each permutation on a new line, in lexicographical order. Each permutation should be formatted as a space-separated string of integers. Example Input: 2 1 2 3 4 Example Output: 1 2 4 3 1 3 2 4 2 1 3 4 2 1 4 3 2 3 1 4 2 4 1 3 3 1 2 4 3 1 4 2 3 2 1 4 3 4 1 2 4 1 2 3 4 1 3 2 4 2 1 3 4 3 1 2