008. N-Dimensional Distance

008. N-Dimensional Distance

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Calculate the distance between two points of a specified dimension. The common distance formula still applies to higher dimensional points with a small modification. You will input two points and display the distance between them as you normally would with the distance formula.

The n-dimensional distance formula can be expressed as

𝑑(𝑝,𝑞)=(𝑞1−𝑝1)2+(𝑞2−𝑝2)2+...+(𝑞𝑛−𝑝𝑛)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√$d(p,q)=\sqrt{(q_1-p_1{)}^2+(q_2-p_2{)}^2+...+(q_n-p_n{)}^2}$

or in other terms:

∑𝑛𝑖=1(𝑞𝑖−𝑝𝑖)2‾‾‾‾‾‾‾‾‾‾‾‾‾√=𝑑$\sqrt{\sum _{i=1}^n(q_i-p_i{)}^2}=d$

Remember that math.sqrt will calculate the square root of a number (you also have to add the line import math at the top of the program).

Input

The first line contains the dimension D between 2 and 500. Then, D test cases will follow.

Each test case N will consist of two lines: the value of the first point, and the value of the second point, in the Nth dimension.

Each of these values is an integer between -5000 and 5000, inclusive.

Output

A decimal number N representing the distance between the two points. Do not round your answer.

Examples

input

Copy

2
1
1
1
2

output

Copy

1.0

input

Copy

3
7
4
3
17
6
2

output

Copy

14.866068747318506

input

Copy

4
-2367
-2873
-4279
-2321
-1302
-1341
-2893
651

output

Copy

4080.5951771769764