<|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 0 0 1 1 9 0 5 3 5 0 3 0 4 0 4 0 5 3 5 0 0 1 9 9
Output: 0 0 0 0 0 0 0 0 0 0 9 1 1 9 5 3 5 3 4 4 5 3 5 1 9 9

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

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

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