Mike and his girlfriend Chloe are walking in a park (which is a 2D-plane). They have different starting points(but both of them start at the same time) and different speeds. They walk on different paths.

Path of Mike is (X[1], Y[1]), (X[2], Y[2]) …. (X[N], Y[N]). Starting point of Mike is (X[1], Y[1]) and speed is V_{1}. Path of Chloe is (X[N+1], Y[N+1]), (X[N+2], Y[N+2]) …. (X[2*N], Y[2*N]). Starting point of Chloe is (X[N+1], Y[N+1]) and speed is V_{2}.

After reaching the end of the path, the person stays there. You need to find the closest distance between them during their walk. Print the distance correct till 4 decimal places.

Input format :

First line of input contains integer T, the number of test cases.

The first line of each test case contains three space separated integers N, V_{1} and V_{2}.

Next 2N lines have two integers each, X[i] and Y[i].

Output Format :

Constraints :

1 ≤ T ≤ 5

1 ≤ N ≤ 100000

1 ≤ X[i], Y[i] ≤ 10^{9}

1 ≤ V_{1}, V_{2} ≤ 10^{9}

Sample Input :

1

4 1 1

0 0

2 2

1 2

0 1

4 0

2 0

3 1

3 2

Sample Output :

1.5307

ID

SUBMITTED AT

STATUS

LANGUAGE

TIME

MEMORY USED

USER

TIME

STATUS

LANGUAGE

TIME

MEMORY USED

5 months ago

cpp

0.79 sec

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