<|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:  8 5 5 8 8 1 8 5 3 4 2 7 7 2 7 4 9 8 0 0 0 0 0 0 0 0 0 0 0
Output: 0 0 8 5 5 8 8 1 8 5 3 4 2 7 7 2 7 4 9 8 0 0 0 0 0 0 0 0 0

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

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

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