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

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

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

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 0 0 0 0 4 6 9 2 1 7 1 7 3 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