Generate Lexicographically Sorted Permutations

Given a positive integer \( n \), generate all permutations of the numbers from 1 to \( n \) in lexicographic (dictionary) order. If \( n \) is not a valid positive integer (i.e., if \( n\le0 \) or \( n \) cannot be parsed as an integer), output an empty list: [].

For example:

• Input: 3, Output:

  1 2 3
  1 3 2
  2 1 3
  2 3 1
  3 1 2
  3 2 1
      

• Input: 1, Output:

  1
      

• Input: 0, Output: []
• Input: -1, Output: []

All output permutations must be sorted in lexicographic order. Note that a lexicographic order means that the permutation \( A = [a_1, a_2, \dots, a_n] \) comes before \( B = [b_1, b_2, \dots, b_n] \) if there exists an index \( i \) such that \( a_j = b_j \) for every \( j < i \) and \( a_i < b_i \).

inputFormat

The input is provided via standard input (stdin) as a single line containing the value \( n \). This value should be parsed as an integer. If parsing fails or if \( n \) is not greater than 0, the program should output an empty list ([]).

outputFormat

If \( n \) is a valid positive integer, output each permutation on a separate line to standard output (stdout). The numbers within each permutation must be separated by a single space. If \( n \) is invalid, output [].

## sample

3

1 2 3
1 3 2
2 1 3
2 3 1
3 1 2
3 2 1

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