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

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

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

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