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

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

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

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 1 6 4 9 9 1 9 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