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

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

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

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