<|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 7 8 1 8 7 5 9 7 7 8 4 6 9 4 9 4 2 6 0 0 0 0 0 9 3 2 7 4 8
Output: 8 9 7 8 1 8 7 5 9 7 7 8 4 6 9 4 9 4 2 6 0 0 0 0 0 9 3 2 7 4

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
7 7 2 4 8 7 6 9 1 5 7 2 6 7 8 7 1 7 1 6 7 5 1 4 4 2 6 5 3 9
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