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 0 0 0 0 0 0 0 0 0 4 7 9 0 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 7 9

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
4 1 1 3 5 3 6 7 3 9 3 7 3 2 3 0 0 0 0 0 0 0 0 0 0 4 1 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