TREE1  Tree
Consider an nvertex binary search tree T containing n keys 1, 2 ... n. A permutation p = [p_{1} ... p_{n}] of the integers 1, 2 ... n is said to be consistent with the tree T if the tree can be built from the empty one as the result of inserting integers p_{1}, p_{2} ... p_{n}. Find how many permutations are consistent with the tree T.
Illustration
Exactly 2 permutations are consistent with the tree in the figure below.
Task
Write a program that for each data set from a sequence of several data sets:
 reads from the input file a description of an input tree T,
 computes the number of permutations consistent with T,
 writes the result to output.
Input
The first line of the input file contains one positive integer d not larger than 10. This is the number of data sets. The data sets follow. Each set of data occupies two consecutive lines of the input file. The first line contains only one integer n, 1 <= n <= 30. This is the number of vertices of the tree. The second line contains a sequence of n integers separated by single spaces. The integers are keys in the input tree given in the prefix order. The first integer in the sequence is the key from the root of the tree. It is followed by the keys from the left subtree written in the prefix order. The sequence ends with the keys from the right subtree, also given in the prefix order.
Output
For each i = 1 ... d, your program should write to the ith line of output the number of permutations consistent with the tree described in the ith data set.
Example
Sample input: 5 3 2 1 3 3 1 2 3 1 1 4 2 1 3 4 4 1 4 2 3 Sample output: 2 1 1 3 1
hide comments
iostream:
20121228 08:13:53
what to do for equal numbers?? 

!n[10]se:
20110223 00:40:27
Yes the answer exceeds LL. 

:D:
20110127 07:21:38
No, the description says only permutations of <1;N> are given. 

tarun goyal:
20110127 07:04:16
can 2 numbers be equal??? 

Kedar Joglekar:
20101111 06:58:41
Does answer exceed the unsigned long long int range? 

pulkit agarwal:
20100315 23:05:52
unsigned even doesn't fit I suppose 

Cihad OGE:
20091112 10:11:33
is answer exceed long long int ?? 
Added by:  adrian 
Date:  20040608 
Time limit:  5s 
Source limit:  50000B 
Memory limit:  1536MB 
Cluster:  Cube (Intel G860) 
Languages:  All except: NODEJS PERL6 VB.NET 
Resource:  III Polish Collegiate Team Programming Contest (AMPPZ), 1998 