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

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

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

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