ASSIGN - Assignments

Problem

Your task will be to calculate number of different assignments of n different topics to n students such that everybody gets exactly one topic he likes.

Input

First line of input contains number of test cases c (1<=c<=80). Each test case begins with number of students n (1<=n<=20). Each of the next n lines contains n integers describing preferences of one student. 1 at the ith position means that this student likes ith topic, 0 means that he definitely doesn't want to take it.

Output

For each test case output number of different assignments (it will fit in a signed 64-bit integer).

Example

Input:
3
3
1 1 1
1 1 1
1 1 1
11
1 0 0 1 0 0 0 0 0 1 1 
1 1 1 1 1 0 1 0 1 0 0 
1 0 0 1 0 0 1 1 0 1 0 
1 0 1 1 1 0 1 1 0 1 1 
0 1 1 1 0 1 0 0 1 1 1 
1 1 1 0 0 1 0 0 0 0 0 
0 0 0 0 1 0 1 0 0 0 1 
1 0 1 1 0 0 0 0 0 0 1 
0 0 1 0 1 1 0 0 0 1 1 
1 1 1 0 0 0 1 0 1 0 1 
1 0 0 0 1 1 1 1 0 0 0 
11
0 1 1 1 0 1 0 0 0 1 0 
0 0 1 1 1 1 1 1 1 1 1 
1 1 0 1 0 0 0 0 0 1 0 
0 1 0 1 0 1 0 1 0 1 1 
1 0 0 1 0 0 0 0 1 0 1 
0 0 1 0 1 1 0 0 0 0 1 
1 0 1 0 1 1 1 0 1 1 0 
1 0 1 1 0 1 1 0 0 1 0 
0 0 1 1 0 1 1 1 1 1 1 
0 1 0 0 0 0 0 0 0 1 1 
0 1 1 0 0 0 0 0 1 0 1 

Output:
6
7588
7426


Added by:gawry
Date:2005-10-08
Time limit:2.997s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL6 VB.NET

hide comments
2020-01-29 10:25:44
Please recommend questions similar to this
2020-01-24 10:35:19
DP with Bitmasking will do:)
2019-11-24 16:47:46
@nani_99...DCT would make the compile-time <.01 s....very bad question since brute force also give AC
2019-11-24 16:43:12
No, you are wrong @anonymous_09.You should use convolution
2019-11-16 21:38:27
(2^n)*n*c then fourier transformation gives AC in one go...!!!
2019-10-11 16:02:19
Declared int instead of long long int, this will cause overflow . and lead to WA :)
2019-08-20 16:08:57
sometimes top down is better...(*..*)
2019-08-15 22:55:43
AC IN ONE GO...!!
2019-08-15 16:16:48
TLE then i read comments
TLE then i carefully read comments about 1D dp
AC :)

Last edit: 2019-08-15 16:17:02
2019-05-31 19:51:31
the top down approach gives TLE.... don't know why
bottom up - AC

Last edit: 2019-05-31 20:29:24
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