<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
6 4 4 1 9 8 2 3 3 2 3 5 5 9 4 1 5 5 1 7 2 3 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user