Sudoku Validator

You are given a 9x9 Sudoku puzzle. Your task is to determine whether the puzzle is valid, solved, or invalid.

A Sudoku puzzle is composed of 9 rows and 9 columns with cells containing digits from 1 to 9 or 0 representing an empty cell. The puzzle must satisfy the following conditions:

• Each row must contain unique non-zero values.
• Each column must contain unique non-zero values.
• Each of the nine $3\times3$ subgrids must contain unique non-zero values.

If all conditions are satisfied and there is at least one 0 present, output Valid Sudoku. If all conditions are satisfied and there are no 0's, output Sudoku Solved. Otherwise, output Invalid Sudoku.

inputFormat

The input consists of 9 lines. Each line contains 9 integers separated by a space representing a row of the puzzle. The integer 0 represents an empty cell.

Input is provided via standard input (stdin).

outputFormat

Output a single line that is either Valid Sudoku, Sudoku Solved, or Invalid Sudoku according to the puzzle's correctness.

Output should be written to standard output (stdout).

5 3 0 0 7 0 0 0 0
6 0 0 1 9 5 0 0 0
0 9 8 0 0 0 0 6 0
8 0 0 0 6 0 0 0 3
4 0 0 8 0 3 0 0 1
7 0 0 0 2 0 0 0 6
0 6 0 0 0 0 2 8 0
0 0 0 4 1 9 0 0 5
0 0 0 0 8 0 0 7 9

Valid Sudoku