Merge sort involves splitting the input array into two subarrays recursively, sorting each of them and finally merging two sorted subarrays.

Another idea is to split the input array into three parts as evenly as possible. Then we can try to sort each of them recursively and finally merging three sorted subarrays into one single sorted array.

$1.$ Is this idea correct? Please breifly justify your answer. You may elaborate implementation details of this idea.

$2.$ If this idea is correct. Please analyze the time complexity of the algorithm