<|im_start|>system
You are a helpful assistant. You first think about the reasoning process in the mind and then provides the user with the answer.<|im_end|>
<|im_start|>user
Find the common rule that maps an input grid to an output grid, given the examples below.

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

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

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

Below is a test input grid. Predict the corresponding output grid by applying the rule you found.
Input:
0 0 6 2 4 7 7 9 7 1 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 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>.<|im_end|>
<|im_start|>assistant
Let me solve this step by step.
<think>
user