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

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