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:  7 1 0 0 0 0 0 0 0 0 0 0 0 0 4 2 2 9 3 4 7 4 3 2 3 7 3 9
Output: 0 0 0 0 0 0 0 0 0 0 0 0 4 2 2 9 3 4 7 4 3 2 3 7 3 9 7 1

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

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

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