Two paper planes are thrown upwards simultaneously. You are provided with the following data:

The flight time of both planes is denoted by t (seconds).
The initial coordinates of the first plane are denoted by (b_x, b_y, b_z).
The initial velocity of the first plane is denoted by (\(bv\)_x, \(bv\)_y, \(bv\)_z).
The initial coordinates of the second plane are denoted by (m_x, m_y, m_z).
The initial velocity of the second plane is denoted by (\(mv\)_x, \(mv\)_y, \(mv \)_z).

Write a program to find the minimum distance between the two planes during their flight. Let the jury answer be A and let your answer be B. Your answer will be considered correct if \( |A-B| \le 10^{-6} \)

Input format

First line: t
Second line: Three space-separated integers (denoting b_x, b_y, and b_z)
Third line: Three space-separated integers (denoting \(bv\)_x, \(bv\)_y, and \(bv\)_z)
Fourth line: Three space-separated integers (denoting m_x, m_y, and m_z )
Fifth line: Three space-separated integers (denoting \(mv\)_x, \(mv\)_y, and \(mv\)_z)

Output format

Print the minimum distance between the two planes during their flight.

Constraints

\(0 ≤ t ≤10000\)
\(10000 ≤ b_x , b_y, b_z ≤ 10000 \)
\(10000 ≤ bv_x , bv_y, bv_z ≤ 10000 \)
\(10000 ≤ m_x , m_y, m_z ≤ 10000 \)
\(10000 ≤ mv_x , mv_y, mv_z ≤ 10000 \)