https://acm.cs.nthu.edu.tw/problem/11901/

Description
(目前只有一筆測資，將來會增加到十

Given
A matrix of digits
A starting non-zero digit
Task
Convert all the nonzero digits of the matrix into a tree
Print out the digits according to one of the following tree traversal methods
Level-order-traversal
Pre-order-traversal
Post-order-traversal
Example


Input


Traversal method can be one of the following:

"Level-order-traversal"
"Pre-order-traversal"
"Post-order-traversal"
Output
Repeat the inputs and additionally print out the tree traversal

Sample Input  

6
7 7
1 3
0 0 0 0 0 0 0
2 8 0 1 8 6 0
0 2 0 0 0 4 0
0 2 6 5 6 8 0
0 0 0 5 0 0 0
0 1 8 2 9 9 7
0 0 0 0 0 0 0
Level-order-traversal
7 7
1 3
0 0 0 0 0 0 0
2 8 0 1 8 6 0
0 2 0 0 0 4 0
0 2 6 5 6 8 0
0 0 0 5 0 0 0
0 1 8 2 9 9 7
0 0 0 0 0 0 0
Pre-order-traversal
7 7
1 3
0 0 0 0 0 0 0
2 8 0 1 8 6 0
0 2 0 0 0 4 0
0 2 6 5 6 8 0
0 0 0 5 0 0 0
0 1 8 2 9 9 7
0 0 0 0 0 0 0
Post-order-traversal
7 6
3 3
0 0 0 6 3 0 0
1 0 6 4 0 5 1
2 5 0 2 0 8 0
0 9 7 9 3 4 0
0 0 0 1 0 0 0
0 0 1 6 5 1 7
Pre-order-traversal
7 6
3 3
0 0 0 6 3 0 0
1 0 6 4 0 5 1
2 5 0 2 0 8 0
0 9 7 9 3 4 0
0 0 0 1 0 0 0
0 0 1 6 5 1 7
Post-order-traversal
7 6
3 3
0 0 0 6 3 0 0
1 0 6 4 0 5 1
2 5 0 2 0 8 0
0 9 7 9 3 4 0
0 0 0 1 0 0 0
0 0 1 6 5 1 7
Level-order-traversal

Sample Output  

6
7 7
1 3
0 0 0 0 0 0 0
2 8 0 1 8 6 0
0 2 0 0 0 4 0
0 2 6 5 6 8 0
0 0 0 5 0 0 0
0 1 8 2 9 9 7
0 0 0 0 0 0 0
Level-order-traversal
2 6 2 5 8 5 6 2 2 8 8 9 4 1 9 6 7 8 1
7 7
1 3
0 0 0 0 0 0 0
2 8 0 1 8 6 0
0 2 0 0 0 4 0
0 2 6 5 6 8 0
0 0 0 5 0 0 0
0 1 8 2 9 9 7
0 0 0 0 0 0 0
Pre-order-traversal
2 6 5 5 2 8 1 9 9 7 6 8 4 6 8 1 2 8 2
7 7
1 3
0 0 0 0 0 0 0
2 8 0 1 8 6 0
0 2 0 0 0 4 0
0 2 6 5 6 8 0
0 0 0 5 0 0 0
0 1 8 2 9 9 7
0 0 0 0 0 0 0
Post-order-traversal
1 8 7 9 9 2 5 1 8 6 4 8 6 5 6 2 8 2 2
7 6
3 3
0 0 0 6 3 0 0
1 0 6 4 0 5 1
2 5 0 2 0 8 0
0 9 7 9 3 4 0
0 0 0 1 0 0 0
0 0 1 6 5 1 7
Pre-order-traversal
9 7 9 5 2 1 1 6 1 5 1 7 3 4 8 5 1 2 4 6 6 3
7 6
3 3
0 0 0 6 3 0 0
1 0 6 4 0 5 1
2 5 0 2 0 8 0
0 9 7 9 3 4 0
0 0 0 1 0 0 0
0 0 1 6 5 1 7
Post-order-traversal
1 2 5 9 7 1 7 1 5 6 1 1 5 8 4 3 6 3 6 4 2 9
7 6
3 3
0 0 0 6 3 0 0
1 0 6 4 0 5 1
2 5 0 2 0 8 0
0 9 7 9 3 4 0
0 0 0 1 0 0 0
0 0 1 6 5 1 7
Level-order-traversal
9 7 1 3 2 9 6 4 4 5 1 5 8 6 6 2 1 5 3 1 7 1

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