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# Ninja’s Service Center

Difficulty: MEDIUM
Avg. time to solve
30 min
Success Rate
70%

Problem Statement
Suggest Edit

#### Given a 2-D array ‘location’ where locations[ i ][ 0 ] and location[ i ][ 1 ] denotes the x and y coordinates of position of ‘i-th’ person.You need to return the minimum sum of Euclidian distance of Ninja’s service center from all customers.

The euclidian distance of a point [ x2, y2 ] from [ x1,y1 ] is given as

##### Note
``````You need to round up your answer to the nearest three decimal places.
``````
##### For Example
``````If the position of the customers is [ [ 1,0 ], [ 4,0 ], [ 6,0 ] ], then if Ninja opens his service center at [ 4,0 ] then he will get the minimum sum of euclidian distance = 5.000  from all customers.
``````
##### Input Format
``````The first line contains ‘T’ denoting the number of test cases.
The first line of each test case contains ‘N’ denoting the number of customers.
The next ‘N’ lines contain two space-separated integers ‘ x ’ and ‘ y ’ denoting the coordinates of the position of the customers.
``````
##### Output Format
``````For each test case, print a single integer denoting the minimum sum of Euclidian distance.
Print the output of each test case in a separated line.
``````
##### Constraints
``````1 <= T <= 10
1 <= N <= 10^3
0 <= location[ i ][ 0 ], location[ i ][ 1 ] <= 10^3

Where ‘T’ is the number of test cases, ‘N’ is the number of customers, location[ i ][ 0 ], location[ i ][ 1 ] denotes the ‘ x ’ and ‘ y ’ coordinates of the position of customers.
``````
##### Sample Input 1
``````2
3
2 0
0 0
1 1
1
3 4
``````
##### Sample Output 1
``````2.733
0.000
``````
##### Explanation of Sample Input 1
``````Test Case 1: If NInja opens his service center at [ 1,0 ] then he will get a sum of euclidian distances = 3. But if he opens his center at [ 1, 0.5773 ] then he will get a minimum sum of distances = 2.73205. Round to the nearest three decimal places = 2.733
Test Case 2: There is only one customer so the minimum distance can be ‘0’.
``````
##### Sample Input 2
``````2
3
2 2
3 4
4 1
2
5 3
3 2
``````
##### Sample Output 2
``````4.320
2.237
``````