Advertisement blocking software were detected ;( Please add this webpage to whitelist.

ASSIGN - Assignments

no tags 

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 Pentium G860 3GHz)
Languages:All except: NODEJS PERL 6 VB.net

hide comments
anando_du: 2015-08-31 16:22:18

Top DOwn ... single submission . AC . DP state is important here ....

Abhinandan Agarwal: 2015-08-30 15:46:20

A good problem indeed! Top down -TLE,
Bottom Up - AC

m_elbrbry: 2015-08-18 17:56:19

good one :)

[Mayank Pratap]: 2015-08-05 14:41:28

Took hours to understand the concept of Bitmasks + DP. ..........Coding is easier if u get it... :)

kejriwal: 2015-08-02 12:46:06

nice problem..!! :)

xxbloodysantaxx: 2015-07-16 14:31:27

Took my 8 hours !!
I was able to figure out the solution with complexity O(N^2 * 2^N ) but to achieve O(N*2^N) , I dont know dont waste much time on it just see it :P

sai krishna: 2015-05-29 15:57:07

Any one please explain this test case,unable to understand
1
5
1 1 0 1 0
0 0 1 0 1
1 1 1 0 0
0 0 1 0 1
1 1 1 0 1

Siddharth: 2015-02-28 16:01:13

Same algorithm in JAVA gives TLE... :( Wasted a hell lot of time...

venu gangireddy: 2015-02-27 06:41:01

awesome problem....

Last edit: 2015-02-27 06:41:39
californiagurl: 2015-02-05 12:15:56

beautiful optimization! it wasn't obvious to me, although i had a hunch that my original solution will not pass.