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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 1 2 1 2 1 2 4 9 0 0 0 0 0 0 0 0 1 1 7 3 8 6 1 2 9 7 1 5
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