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

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

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

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