There are $$N$$ towns in a coordinate plane. Town $$i$$ is located at coordinate \((x_i,y_i)\). The distance between town $$i$$ and town $$j$$ is \(|x_i-x_j|+|y_i-y_j|\). Your task is to compute the sum of the distance between each pair of towns.

Input format

• The first line contains an integer $$T$$ denoting the number of test cases.
• The first line of each test case contains an integer $$N$$ denoting the total number of towns.
• Next $$N$$ lines contain two space-separated integers \(x_i\) and \(y_i\) denoting a town at coordinate \((x_i,y_i)\).

Output format

For each test case, print the sum of the distance between each pair of towns in a new line.

Constraints

It is guaranteed that the sum of $$N$$ over $$T$$ test cases does not exceed $$1e6$$.