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

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

Example 3:
Input:  4 4 7 0 0 0 0 0 0 0 0 9 1 4 2 1 2
Output: 1 2 4 4 7 0 0 0 0 0 0 0 0 9 1 4 2

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