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:  2 0 3 5 7 1 9 0 6 0 0 8 0 0 0 3 0 0 0 2 0 0 0 0 7 7 0
Output: 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 3 5 7 1 9 6 8 3 2 7 7

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

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

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