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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 1 6 9 7 1 8 7 5 3 3 6 3 5 3 9 9 1 5 2 4 0 0 3 9 4 8 5 2
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