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:  4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 9 9 1
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 9 9 1 4 0

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 5 8 7 7 3 4 7 6 4 6 5 2 7 2 1 6 2 9 1 6 0 0 0 1 4 9
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