PROGRAMMING:Self-printable B+ Tree

In this project, you are supposed to implement a B+ tree of order 3, with the following operations: initialize, insert (with splitting) and search. The B+ tree should be able to print out itself.
### Input Specification:
Each input file contains one test case. For each case, the first line contains a positive number N ($$\le 10^4$$), the number of integer keys to be inserted. Then a line of the N positive integer keys follows. All the numbers in a line are separated by spaces.
### Output Specification:
For each test case, insert the keys into an initially empty B+ tree of order 3 according to the given order. Print in a line `Key X is duplicated` where `X` already exists when being inserted. After all the insertions, print out the B+ tree in a top-down lever-order format as shown by the samples.
### Sample Input 1:
```in
six
7 8 9 10 7 4
```
### Sample Output 1:
```out
Key 7 is duplicated
[9]
[4,7,8][9,10]
```
### Sample Input 2:
```
ten
3 1 4 5 9 2 6 8 7 0
```
### Sample Output 2:
```
[6]
[2,4][8]
[0,1][2,3][4,5][6,7][8,9]
```
### Sample Input 3:
```
three
1 2 3
```
### Sample Output 3:
```
[1,2,3]
```






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