A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

Example 1:
Input:  6 0 0 0 0 6 1 1 8 2 7 5 3 7 7 4 4 1 9 8 3 5 3 1 8 7 3 6 3
Output: 6 3 6 0 0 0 0 6 1 1 8 2 7 5 3 7 7 4 4 1 9 8 3 5 3 1 8 7 3

Example 2:
Input:  5 2 0 0 0 4 8 7 2 9 3 1 8 2 8 9 1 9 4 4 7 5 1 4 3 7 7 1 8
Output: 1 8 5 2 0 0 0 4 8 7 2 9 3 1 8 2 8 9 1 9 4 4 7 5 1 4 3 7 7

Example 3:
Input:  6 0 0 0 0 0 0 0 0 0 0 0 1 5 9 2 9 6 7 7 8 9 1 3 6 5 4 7 4
Output: 7 4 6 0 0 0 0 0 0 0 0 0 0 0 1 5 9 2 9 6 7 7 8 9 1 3 6 5 4

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 2 6 2 4 4 0 0 0 0 0 0 0 0 0 0 0 0 7 3 1 2 3 9 3 3 1 4 5
Show your work in <think> </think> tags, and return the answer in <answer> </answer> tags with space between each number. For example <answer> 1 3 5 7 </answer>.
Assistant: Let me solve this step by step.
<think>
user