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

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

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

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