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

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

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

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