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Ninja And The Clan

Difficulty: MEDIUM
Contributed By
Avg. time to solve
24 min
Success Rate
70%

Problem Statement

There are ‘N’ Ninjas in a clan and the clan leader wants to assign ‘N’ tasks to each of the Ninjas. There is a ‘cost’ matrix of size ‘N’ x ‘N’, where ‘COST[i][j]’ denotes the cost of ‘i’th Ninja completing the ‘j’th task. The leader wants to assign the task in such a way that the total cost is minimized.

Note that each task is assigned to a single Ninja, and each Ninja will only be allotted a single task.

EXAMPLE:
Input: 
'N' = 3
‘COST’ = [[1 2 3],
          [6 5 6],
          [3 8 9]]

Output: 11

A possible assignment is:
Assign task 1 to ninja 3, task 2 to ninja 1 and task 3 to ninja 2, total cost = 3 + 2 + 6 = 11
Input Format :
The first line will contain the integer 'T', the number of test cases. For each test case

The first line of each test case an integer ‘N’ denoting the number of Ninjas and tasks.
The next ‘N’ lines  contain ‘N’ integers denoting the cost of ith Ninja completing the jth task.
Output format :
For each test case, print a single integer denoting the minimum cost of the assignment.
Note :
You don't need to print anything. It has already been taken care of. Just implement the given function.
Constraints :
1 <= 'T' <= 10
1 <= 'N' <= 18
1 <= 'COST[i][j]' <= 10^5
Time Limit: 1 sec
Sample Input 1 :
2
2
10 13
12 14
3
1 1 1
2 2 1
1 2 1
Sample Output 1 :
24
3
Explanation Of Sample Input 1 :
For the first test case, a possible assignment can be:
Ninja 1 to task 1, Ninja 2 to task 2.

For the second test case, a possible assignment can be:
Ninja 1 to task 2, Ninja 2 to task 3, and Ninja 3 to task 1.
Sample Input 2 :
2
3
2 4 6
8 4 2
8 4 8
5
1 3 5 7 4
3 4 9 10 11
1 2 1 2 1
5 4 8 3 3
6 6 6 6 6
Sample Output 2 :
8
15
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