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

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

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

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