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

Example 2:
Input:  1 8 1 1 5 8 9 8 0 0 0 0 0 0 0 5 1 5 2
Output: 8 1 1 5 8 9 8 0 0 0 0 0 0 0 5 1 5 2 1

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

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