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

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

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

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