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

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

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