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

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

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

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