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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 8 7 3 2 9 2 4 3 5 6 2 5 1 4
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