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

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

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

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 4 6 7 5 2 1 5 1 5 5 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