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

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

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

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