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 7 9 4 1 7 1 1 6 9 7 0 0 0 0 0 0 0 0 0 0 0 3 9
Output: 9 9 7 9 4 1 7 1 1 6 9 7 0 0 0 0 0 0 0 0 0 0 0 3

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

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

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 3 3 2 9 7 7 9 2 4 9
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