<|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 6 1 9 7 1 6 4 4 2 5 5 4 0 0 0 0 0 0 0 0 0 0 3 8 1 8 7 6
Output: 6 2 6 1 9 7 1 6 4 4 2 5 5 4 0 0 0 0 0 0 0 0 0 0 3 8 1 8 7

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

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

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 5 6 6 6 6 9 2 1 3 8 4 9 5 6 7 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