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

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

Example 3:
Input:  7 7 4 2 4 4 2 7 9 0 0 0 0 7 4 2 4 1 2
Output: 4 1 2 7 7 4 2 4 4 2 7 9 0 0 0 0 7 4 2

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