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

\(1 \le T \le 1000\\ 1 \le N \le 200000\\ 0 \le x_i,y_i \le 1000000000\)

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