PROGRAMMING:Tree maximum product path
The known tree node is an integer not equal to 0. Write a program to find the path with the largest product in the non empty tree. The "path" of this problem is defined as the sequence of nodes in the tree_{ i},...,v_{ j} $$, the former node in the sequence is the parent node of the latter node, but the path does not necessarily start with the root node or end with the leaf node. The product of a path is defined as the product of the data values of all nodes in the path. For example, for the tree T shown in Fig. 1 (a), the path of maximum product is 8-5-6.
###Input format:
The input is a group of integers separated by spaces, the number of which is no more than 100, indicating the first root sequence of binary tree with null pointer information, where null pointer information is represented by 0.
Note: we know that the left child of the node in the binary tree corresponds to the left child of the node in the tree, and the right child of the node in the binary tree corresponds to the right brother of the node in the tree. Then we can use the method of "building binary tree based on the first root sequence with null pointer information" to construct the left child right brother storage structure of the corresponding tree. As shown in Figure 1 (a), 8 5 10 6 0 2 0 3 4 0 7 0 0 0 0 0 0 0 corresponds to the tree as shown in Figure 1 (b).
###Output format:
The output is two lines. The first line is the maximum value of the path product of the tree, and the second line is a set of integers with space interval, that is, the node value contained in the maximum product path (output in ascending order according to the number of layers)** If there are multiple paths satisfying the conditions, the shortest path (including the least number of nodes) will be output. If there are multiple shortest paths, the shortest path on the left will be output**
###Input sample 1:
```in
8 5 1 0 6 0 2 0 0 3 4 0 0 7 0 0 0
```
###Output sample 1:
```out
two hundred and forty
8 5 6
```
###Input sample 2:
```in
1 2 0 3 0 4 0 0 0
```
###Output sample 2:
```out
four
four
```
answer：If there is no answer, please comment
###Input format:
The input is a group of integers separated by spaces, the number of which is no more than 100, indicating the first root sequence of binary tree with null pointer information, where null pointer information is represented by 0.
Note: we know that the left child of the node in the binary tree corresponds to the left child of the node in the tree, and the right child of the node in the binary tree corresponds to the right brother of the node in the tree. Then we can use the method of "building binary tree based on the first root sequence with null pointer information" to construct the left child right brother storage structure of the corresponding tree. As shown in Figure 1 (a), 8 5 10 6 0 2 0 3 4 0 7 0 0 0 0 0 0 0 corresponds to the tree as shown in Figure 1 (b).
###Output format:
The output is two lines. The first line is the maximum value of the path product of the tree, and the second line is a set of integers with space interval, that is, the node value contained in the maximum product path (output in ascending order according to the number of layers)** If there are multiple paths satisfying the conditions, the shortest path (including the least number of nodes) will be output. If there are multiple shortest paths, the shortest path on the left will be output**
###Input sample 1:
```in
8 5 1 0 6 0 2 0 0 3 4 0 0 7 0 0 0
```
###Output sample 1:
```out
two hundred and forty
8 5 6
```
###Input sample 2:
```in
1 2 0 3 0 4 0 0 0
```
###Output sample 2:
```out
four
four
```
answer：If there is no answer, please comment