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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 4 2 0 0 0 0 4 2 5 3 5 8 3 0 0 0 5 5 0 1 0 0 7 0 8 0
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