You must write a program that solves a 4×4 sudoku grid that have only one solution. A solved sudoku is a latin square for which each 2×2 corner square must also contain all the digits 1 to 4.

INPUT:

You are given a 4×4 grid, the empty cells are represented by 0. For example: 2000 0130 3001 0240

OUTPUT:

The output must be the only solution, all the zeros must be filled by the correct digits. Here: 2314 4132 3421 1243