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
adam____: 2021-08-27 16:51:29

AC in one, the bitmasks are a really big hint
Used recursive DP, and top down i think

tropo_sphere: 2021-06-26 16:53:19

Can explain O(2^n*n) complexity approach plz! Mine was O(n*n*2^n) with optimization.

null12_21: 2021-06-08 08:11:50

use row...keep a mask to check which index you have been taken i mean which assignment...mask can use with bit operation. use a for loop between the recursive solution. if you on a position on mask dont forget to off it after the iteration

anupam_akib: 2021-05-22 20:14:11

Finally got AC after 1 TLE and 2 WA. Nice problem for beginners who started solving DP with bitmasks.

saurabh_38: 2021-02-18 10:20:22

use-> unsigned long long
Good problem

dhruvgheewala: 2021-01-30 12:48:33

@brokeboy, my code having similar complexities, but I am getting TLE. Do you have any clue, I am using a 2-d vector and adjacency matrix to store preferences.

Edit: how you got AC with that complexity( Time: O( 2 ^ 20 * n * n * c), 2 ^ 20 * n * n * c = 1M * 20 * 20 * 80 = 1M * 32 * 1000 = 32 * 10 ^ 9)

Last edit: 2021-01-30 12:53:27
ayushpandia: 2021-01-18 14:36:31

Really nice problem

ant_2001: 2021-01-17 13:11:25

I am using DP+bitmask, long long ......test cases give correct answer but I am still getting WA . Please help!

lamda_cdm_10: 2020-10-28 14:29:05

Nice problem for people who are starting to learn bitmasks... has a tight time limit ... enjoyed solving it.

pranavsindura: 2020-09-05 10:50:20

Both top down and bottom up work.


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