<|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 6 0 0 0 0 0 0 0 4 1 5 6 7 4 4 5 5 6
Output: 5 6 9 6 0 0 0 0 0 0 0 4 1 5 6 7 4 4 5

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

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

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