A conversation between User and Assistant. The user asks a question, and the Assistant solves it. The assistant first thinks about the reasoning process in the mind and then provides the user with the answer.
User: Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 1 7 6 4 5 7 0 0 0 0 0 0 0 0 0 0 0 0 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>.
Assistant: Let me solve this step by step.
<think>
user