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

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

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