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

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

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

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 4 6 9 0 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