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


hide comments
kshubham02: 2017-03-24 14:00:59

O(2^N * N) solution by clearing complete DP array every time ===> TLE
O(2^N * N) solution by clearing DP array only upto n and (1<<n) every time ===> AC 2.00
Can't seem to understand which approach runs in smaller time :/

cake_is_a_lie: 2017-02-24 03:30:41

Wow, AC and #2 time on 1st try :-D
Bit operations galore and O(2^N * N), as opposed to O(2^N * N^2).
A bit of combinatorics and common sense help a lot in making that solution faster; so does __builtin_popcount.

Last edit: 2017-02-24 03:35:22
chapaniyash: 2017-02-02 23:26:11

to count no of 1s in mask use __builtin_popcount(mask);

practice9535: 2017-01-18 06:33:35

how people are solving it in 0.15 sec... mine solution dp(top down) took 2.5 secs.... is there any better and optimal method to solve??????/

saurav786: 2016-11-07 21:31:07

Topdown+bitmasking :-D

poomrokc: 2016-10-15 08:20:36

My O(2^n*n) Gets tle Xp for each case lol

dev: 2016-10-10 16:49:52

Very Nice DP + BitMasking !
O(2^n * n*n ) will give Tle.

hamjosh1: 2016-09-22 15:12:53

learned new things :'D

srinath: 2016-09-21 11:52:19

Using map gives TLE. Use vector instead.

darwinthamil: 2016-07-27 15:32:52

@vikikkdi : seri


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