Maybe you know about the game called Darts. The goal of the game is to hit a circular target, which is called a dartboard. To do so you should take a dart and throw it to the dartboard. Of course, it takes time to learn how to hit the dartboard. And your task is to speed the learning by writing a program that determines if a dart will hit or miss the dartboard.

Let's make some assumptions about the objects under consideration.

1. A dartboard is a circular part of a plane. It is defined by coordinates of its center (C_x, C_y and C_z), radius R, and coordinates of a vector that is orthogonal to the plane of the dartboard (N_x, N_y and N_z).
2. A dart is a point that moves according the following equations:
   M_x = S_x + V_x·t
   M_y = S_y + V_y·t
   M_z = S_z + V_z·t − (g/2)·t²
   Here S_x, S_y, and S_z are coordinates of initial position of the dart, V_x, V_y, and V_z are components of initial velocity of the dart, M_x, M_y, and M_z are coordinates of the point where the dart will be at time t, g is the acceleration of gravity and is assumed to be equal to 10.
3. You may assume that the dart is thrown with a nonzero horizontal component (i.e. V_x or V_y is non-zero).
4. You may assume no friction.
5. To hit the dartboard the dart should hit it strictly inside boundary from any side.
6. Initially the dart is not inside the dartboard's boundary.

Input contains 13 real numbers. They are (according to notation given before):

C_x C_y C_z N_x N_y N_z R
S_x S_y S_z V_x V_y V_z

All numbers are not greater than 500 in their absolute values and given with at most 4 digits after decimal point. R > 0.

Output should contain the only word “HIT” if dart hits the dartboard, and word “MISSED” otherwise.