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.

- 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}).
- 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)·*t*^{2}

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.
- You may assume that the dart is thrown with a nonzero horizontal component (i.e.
*V*_{x} or *V*_{y} is non-zero).
- You may assume no friction.
- To hit the dartboard the dart should hit it strictly inside boundary from any side.
- Initially the dart is not inside the dartboard's boundary.

### Input

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

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

### Sample

input | output |
---|

47 0 -72 1 0 1 4.25
0 0 0 10 0 10 | HIT |

**Problem Author: **Alexander Klepinin

**Problem Source: **USU Open Collegiate Programming Contest March'2001 Senior Session