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

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

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