Fools Club

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You joined a FOOLS  FOOTBALL CLUB as a coach. There are N players in the club, each one of the player either belongs to TEAM A or TEAM B. None of the players are equal in strength pairwise.
Since you are new to the club you dont know the players strengths.
So you start asking every player a question " HOW MANY PLAYERS IN YOUR TEAM(TEAM A or TEAM B) ARE BETTER THAN YOU?". Now each player either of TEAM A or B tells the number of players better than him in his TEAM respectively. Since the players know each of thier teammates so they know how many are better than him.(Players can lie too)
Let the answer given by the kth player be answer[k]. Given these numbers, print the number of configurations resulting in exactly those numbers, assuming everone tells the truth.
Two configurations are different if the kth player is of TEAM A in one configuration and of TEAM B in other configuration.
Input
First line of input contains number of test cases T.
Then each of the next T lines contains an integer N (total number of players in CLUB) and then N integers(ANSWER ARRAY) separated by space in the same line.
Output
For each Test Case print the number of configurations in a new line.
Constraints
 1 ≤ T ≤ 10000
 1 ≤ N ≤ 42
Example
Input: 3 5 0 1 2 3 4 11 12 11 10 5 4 3 2 1 0 13 11 4 0 1 0 1 Output: 2 0 4
Explanation
In first test case either all the players of team 1 or team 2.
In second test case there are only 11 players , So some players are lying.
In the third test case There are two Players of team A and two Players of team B.
Author:  jammeron 
Tags  jammeron 
Date Added:  9042015 
Time Limit:  5 sec 
Source Limit:  50000 Bytes 
Languages:  C, JAVA, PYTH, PYTH 3.6, CAML 
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