Hard

33.03%

Given a matrix M of size N where M[i][j] denotes the cost of moving from city i to city j. Your task is to complete a tour from the city 0 (0 based index) to all other cities such that you visit each city atmost once and then at the end come back to city 0 in min cost.

**Input:**

The first line of input contains an integer T denoting the no of test cases. Then T test cases follow. Each test case contains an integer N denoting the size of the matrix then in the next line are N*N space separated values of the matrix M.

** **

**Output:**

For each test case print the required result denoting the min cost of the tour in a new line.

**Constraints:**

1<=T<=15

1<=N<=12

1<=M[][]<=10000

**Example:
Input:**

2

2

0 111 112 0

3

0 1000 5000 5000 0 1000 1000 5000 0

223

3000