#include <iostream>
#include <cmath>
using namespace std;
typedef double Real;
const Real EPS = 1e-5;
struct plane{
  Real a, b, c, d;
plane() {}
plane(Real a, Real b, Real c, Real d) : a(a), b(b), c(c), d(d) {}
};
struct vect {
  Real x, y, z;
vect(Real x = 0, Real y = 0, Real z = 0) : x(x), y(y), z(z) {}
void add(vect& a){
    x += a.x;
    y += a.y;
    z += a.z;
  }
void sub(vect& a){
    x -= a.x;
    y -= a.y;
    z -= a.z;
  }
void mul(Real a){
    x *= a;
    y *= a;
    z *= a;
  }
void div(Real a){
    x /= a;
    y /= a;
    z /= a;
  }
  Real dot(vect& a){
return (x * a.x + y * a.y + z * a.z);
  }
  Real dot(plane a){
return (x * a.a + y * a.b + z * a.c);
  }
  Real length(){
return sqrt(x * x + y * y + z * z);
  }
  Real dist(vect& a){
    vect c = *this;
    c.sub(a);
return c.length();
  }
  Real& access(int a){
    a %= 3;
if (a == 0) return x;
if (a == 1) return y;
if (a == 2) return z;
return x;
  }
  vect cross(vect& a){
    vect ret;
    vect u = *this, v = a;
    ret.x = u.y * v.z - u.z * v.y;
    ret.y = u.z * v.x - u.x * v.z;
    ret.z = u.x * v.y - u.y * v.x;
return ret;
  }
bool eq(vect& a){
return x == a.x && y == a.y && z == a.z;
  }
};
ostream &operator<<(ostream &os, const vect &a) { os << "(" << a.x << ", " << a.y << ", " << a.z << ")"; return os; }
struct tri{
  vect p0, p1, p2;
tri(vect a, vect b, vect c) : p0(a), p1(b), p2(c) {}
  vect normal(){
    Real a = ((p1.y - p0.y) * (p2.z - p0.z)) - ((p2.y - p0.y) * (p1.z - p0.z));
    Real b = ((p1.z - p0.z) * (p2.x - p0.x)) - ((p2.z - p0.z) * (p1.x - p0.x));
    Real c = ((p1.x - p0.x) * (p2.y - p0.y)) - ((p2.x - p0.x) * (p1.y - p0.y));
    vect ret(a, b, c);
// cout << "ret : " << ret << ", length = " << ret.length() << endl;
    ret.div(ret.length());
return ret;
  }
  Real area(){
    Real a, b, c, s;
    a = p0.dist(p1), b = p1.dist(p2), c = p2.dist(p0);
    s = (a + b + c) / 2;
return sqrt(s * (s - a) * (s - b) * (s - c));
  }
};
bool intersect(vect n, vect A, vect B, vect v1, vect *ret)
{
  vect AP = v1; AP.sub(A);
  vect BP = v1; BP.sub(B);
  Real dot_APN = AP.dot(n), dot_BPN = BP.dot(n);
if (abs(dot_APN) < EPS && abs(dot_BPN) < EPS){
// cout << "double zero" << endl;
return false;
  }
else if ((dot_APN - EPS <= 0.0 && 0.0 <= dot_BPN + EPS) || (dot_BPN - EPS <= 0.0 && 0.0 <= dot_APN + EPS)){
// RINPANA
  }
else {
// cout << "same side" << endl;
return false;
  }
  vect AB = B; AB.sub(A);
  Real h = abs(dot_APN) / (abs(dot_APN) + abs(dot_BPN));
// cout << "AP : " << AP << " BP : " << BP << endl;
// cout << "dot_APN = " << dot_APN << ", dot_BPN = " << dot_BPN << endl;
// cout << "AB : " << AB << endl;
  ret->x = A.x + (AB.x * h);
  ret->y = A.y + (AB.y * h);
  ret->z = A.z + (AB.z * h);
return true;
}
int main()
{
  Real x, y, z;
while (cin >> x){
if (cin.eof()) break;
    cin >> y >> z;      vect uaz_(x, y, z);
    cin >> x >> y >> z;    vect enemy_(x, y, z);
    cin >> x >> y >> z;    vect v1_(x, y, z);
    cin >> x >> y >> z;    vect v2_(x, y, z);
    cin >> x >> y >> z;    vect v3_(x, y, z);
    tri barrier(v1_, v2_, v3_);
    vect n = barrier.normal();
    vect uaz = uaz_, v1 = v1_;
    vect v = uaz_;
    v.sub(enemy_);
    uaz.sub(v1);
// cout << n << endl;
bool ok = true;
if (abs(v.dot(n)) < EPS){
// cout << "zero" << endl;
    }
else {
// Real t = (uaz.dot(n)) / (v.dot(n));
// // cout << "DEBUG ***" << t << " " << dst << endl;
// if (t < 0){
//   // cout << "back" << endl;
//   ok = false;
// }
// else if (dst < t + EPS){
//   // cout << "over" << endl;
//   ok = false;
// }
      vect inter;
if (!intersect(n, uaz_, enemy_, v1_, &inter)){
// NIKOMAKI
// cout << "empty" << endl;
      }
else {
// cout << "intersect point : " << inter << endl;
// Q, v1, v2
        Real a, b, c, s;
        a = inter.dist(v1_), b = v1_.dist(v2_), c = v2_.dist(inter);
        s = (a + b + c) / 2;
        Real T1 = sqrt(s * (s - a) * (s - b) * (s - c));
// Q, v2, v3
        a = inter.dist(v2_), b = v2_.dist(v3_), c = v3_.dist(inter);
        s = (a + b + c) / 2;
        Real T2 = sqrt(s * (s - a) * (s - b) * (s - c));
// Q, v3, v1
        a = inter.dist(v3_), b = v3_.dist(v1_), c = v1_.dist(inter);
        s = (a + b + c) / 2;
        Real T3 = sqrt(s * (s - a) * (s - b) * (s - c));
// cout << T1 << " " << T2 << " " << T3 << " " << barrier.area() << endl;
if ((T1 + T2 + T3) < barrier.area() + EPS){
// inside
          ok = false;
        }
      }
    }
if (ok){
      cout << "HIT" << endl;
    }
else {
      cout << "MISS" << endl;
    }
  }
return 0;
}
### Prompt

Generate a Cpp solution to the following problem:

Stellar history 2005.11.5. You are about to engage an enemy spacecraft as the captain of the UAZ Advance spacecraft. Fortunately, the enemy spaceship is still unnoticed. In addition, the space coordinates of the enemy are already known, and the "feather cannon" that emits a powerful straight beam is ready to launch. After that, I just issue a launch command.

However, there is an energy barrier installed by the enemy in outer space. The barrier is triangular and bounces off the "feather cannon" beam. Also, if the beam hits the barrier, the enemy will notice and escape. If you cannot determine that you will hit in advance, you will not be able to issue a launch command.

Therefore, enter the cosmic coordinates (three-dimensional coordinates x, y, z) of the UAZ Advance, enemy, and barrier positions, and if the beam avoids the barrier and hits the enemy, "HIT", if it hits the barrier " Create a program that outputs "MISS".

However, the barrier is only for those that look like a triangle from the Advance issue, and nothing that looks like a line segment is crushed. Barriers are also valid at boundaries containing triangular vertices and shall bounce the beam. Also, if the enemy is in the barrier, output "MISS".

Constraints

* -100 ≤ x, y, z ≤ 100
* The UAZ Advance and the enemy are never in the same position.

Input

The format of the input data is as follows:

The first line is the coordinates of UAZ Advance (x, y, z) (integer, half-width space delimited)
The second line is the coordinates of the enemy (x, y, z) (integer, half-width space delimiter)
The third line is the coordinates of vertex 1 of the barrier (x, y, z) (integer, half-width space delimiter)
The fourth line is the coordinates (x, y, z) of the vertex 2 of the barrier (integer, half-width space delimiter)
The fifth line is the coordinates (x, y, z) of the vertex 3 of the barrier (integer, half-width space delimiter)

Output

Output on one line with HIT or MISS.

Examples

Input

-10 0 0
10 0 0
0 10 0
0 10 10
0 0 10


Output

HIT


Input

-10 6 6
10 6 6
0 10 0
0 10 10
0 0 10


Output

MISS

### Response

```cpp
#include <iostream>
#include <cmath>
using namespace std;
typedef double Real;
const Real EPS = 1e-5;
struct plane{
  Real a, b, c, d;
plane() {}
plane(Real a, Real b, Real c, Real d) : a(a), b(b), c(c), d(d) {}
};
struct vect {
  Real x, y, z;
vect(Real x = 0, Real y = 0, Real z = 0) : x(x), y(y), z(z) {}
void add(vect& a){
    x += a.x;
    y += a.y;
    z += a.z;
  }
void sub(vect& a){
    x -= a.x;
    y -= a.y;
    z -= a.z;
  }
void mul(Real a){
    x *= a;
    y *= a;
    z *= a;
  }
void div(Real a){
    x /= a;
    y /= a;
    z /= a;
  }
  Real dot(vect& a){
return (x * a.x + y * a.y + z * a.z);
  }
  Real dot(plane a){
return (x * a.a + y * a.b + z * a.c);
  }
  Real length(){
return sqrt(x * x + y * y + z * z);
  }
  Real dist(vect& a){
    vect c = *this;
    c.sub(a);
return c.length();
  }
  Real& access(int a){
    a %= 3;
if (a == 0) return x;
if (a == 1) return y;
if (a == 2) return z;
return x;
  }
  vect cross(vect& a){
    vect ret;
    vect u = *this, v = a;
    ret.x = u.y * v.z - u.z * v.y;
    ret.y = u.z * v.x - u.x * v.z;
    ret.z = u.x * v.y - u.y * v.x;
return ret;
  }
bool eq(vect& a){
return x == a.x && y == a.y && z == a.z;
  }
};
ostream &operator<<(ostream &os, const vect &a) { os << "(" << a.x << ", " << a.y << ", " << a.z << ")"; return os; }
struct tri{
  vect p0, p1, p2;
tri(vect a, vect b, vect c) : p0(a), p1(b), p2(c) {}
  vect normal(){
    Real a = ((p1.y - p0.y) * (p2.z - p0.z)) - ((p2.y - p0.y) * (p1.z - p0.z));
    Real b = ((p1.z - p0.z) * (p2.x - p0.x)) - ((p2.z - p0.z) * (p1.x - p0.x));
    Real c = ((p1.x - p0.x) * (p2.y - p0.y)) - ((p2.x - p0.x) * (p1.y - p0.y));
    vect ret(a, b, c);
// cout << "ret : " << ret << ", length = " << ret.length() << endl;
    ret.div(ret.length());
return ret;
  }
  Real area(){
    Real a, b, c, s;
    a = p0.dist(p1), b = p1.dist(p2), c = p2.dist(p0);
    s = (a + b + c) / 2;
return sqrt(s * (s - a) * (s - b) * (s - c));
  }
};
bool intersect(vect n, vect A, vect B, vect v1, vect *ret)
{
  vect AP = v1; AP.sub(A);
  vect BP = v1; BP.sub(B);
  Real dot_APN = AP.dot(n), dot_BPN = BP.dot(n);
if (abs(dot_APN) < EPS && abs(dot_BPN) < EPS){
// cout << "double zero" << endl;
return false;
  }
else if ((dot_APN - EPS <= 0.0 && 0.0 <= dot_BPN + EPS) || (dot_BPN - EPS <= 0.0 && 0.0 <= dot_APN + EPS)){
// RINPANA
  }
else {
// cout << "same side" << endl;
return false;
  }
  vect AB = B; AB.sub(A);
  Real h = abs(dot_APN) / (abs(dot_APN) + abs(dot_BPN));
// cout << "AP : " << AP << " BP : " << BP << endl;
// cout << "dot_APN = " << dot_APN << ", dot_BPN = " << dot_BPN << endl;
// cout << "AB : " << AB << endl;
  ret->x = A.x + (AB.x * h);
  ret->y = A.y + (AB.y * h);
  ret->z = A.z + (AB.z * h);
return true;
}
int main()
{
  Real x, y, z;
while (cin >> x){
if (cin.eof()) break;
    cin >> y >> z;      vect uaz_(x, y, z);
    cin >> x >> y >> z;    vect enemy_(x, y, z);
    cin >> x >> y >> z;    vect v1_(x, y, z);
    cin >> x >> y >> z;    vect v2_(x, y, z);
    cin >> x >> y >> z;    vect v3_(x, y, z);
    tri barrier(v1_, v2_, v3_);
    vect n = barrier.normal();
    vect uaz = uaz_, v1 = v1_;
    vect v = uaz_;
    v.sub(enemy_);
    uaz.sub(v1);
// cout << n << endl;
bool ok = true;
if (abs(v.dot(n)) < EPS){
// cout << "zero" << endl;
    }
else {
// Real t = (uaz.dot(n)) / (v.dot(n));
// // cout << "DEBUG ***" << t << " " << dst << endl;
// if (t < 0){
//   // cout << "back" << endl;
//   ok = false;
// }
// else if (dst < t + EPS){
//   // cout << "over" << endl;
//   ok = false;
// }
      vect inter;
if (!intersect(n, uaz_, enemy_, v1_, &inter)){
// NIKOMAKI
// cout << "empty" << endl;
      }
else {
// cout << "intersect point : " << inter << endl;
// Q, v1, v2
        Real a, b, c, s;
        a = inter.dist(v1_), b = v1_.dist(v2_), c = v2_.dist(inter);
        s = (a + b + c) / 2;
        Real T1 = sqrt(s * (s - a) * (s - b) * (s - c));
// Q, v2, v3
        a = inter.dist(v2_), b = v2_.dist(v3_), c = v3_.dist(inter);
        s = (a + b + c) / 2;
        Real T2 = sqrt(s * (s - a) * (s - b) * (s - c));
// Q, v3, v1
        a = inter.dist(v3_), b = v3_.dist(v1_), c = v1_.dist(inter);
        s = (a + b + c) / 2;
        Real T3 = sqrt(s * (s - a) * (s - b) * (s - c));
// cout << T1 << " " << T2 << " " << T3 << " " << barrier.area() << endl;
if ((T1 + T2 + T3) < barrier.area() + EPS){
// inside
          ok = false;
        }
      }
    }
if (ok){
      cout << "HIT" << endl;
    }
else {
      cout << "MISS" << endl;
    }
  }
return 0;
}
```