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:  0 0 0 0 0 0 0 0 0 0 0 0 0 0 7 4 9 7 8 2 9 4 2 6 9 7 8 8 1 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 7 4 9 7 8 2 9 4 2 6 9 7 8 8 1 0 0 0

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

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

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