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

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

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

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