CT23E  Tree game
Recently Bob invented a new game with a tree (we should remind you, that a tree is a connected graph without cycles): he deletes any (possibly, zero) amount of edges of the tree, and counts the product of sizes of the connected components left after the deletion. Your task is to find out the maximum number that Bob can get in his new game for a given tree.
Input
The first input line contains integer number n (1 ≤ n ≤ 700) — number of vertices in the tree. The following n  1 lines contain the description of the edges. Each line contains the pair of vertices' indexes, joined by an edge, a_{i}, b_{i} (1 ≤ a_{i}, b_{i} ≤ n). It's guaranteed that the graph described in the input is a tree.
Output
Output the only number — the maximum product of sizes of the connected components, that Bob can get after deleting some of the tree's edges.
Example
Input: 8 1 2 1 3 2 4 2 5 3 6 3 7 6 8 Output: 18
hide comments
sans_surya:
20240412 18:41:27
hi 

gejxd:
20230423 14:28:09
How the test samples were obtained？ 

dlwlrm4:
20220719 09:24:11
Let given tree is a degenerated tree. we can get connected components of size two each. so 2 ^ (700 / 2) . So it may require BigInt. Correct me if im wrong. 

jdmoyle:
20210704 21:07:39
how to approach this solution please


cryp_bipul17:
20210602 06:55:17
can some one provide hint for this question


suraj_26:
20200811 05:01:47
hello 
Added by:  Phan Công Minh 
Date:  20100712 
Time limit:  1s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS OBJC PERL6 SQLITE VB.NET 
Resource:  Codeforces 