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

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

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

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