#include <iostream>
#include <climits>
#include <bitset>
#include <utility>
#include <vector>
#include <cmath>

struct vec3
{
  float x;
  float y;
  float z;
};
void normalize (vec3 & vert)
{
  float mag = sqrt(pow(vert.x, 2) + pow(vert.y, 2) + pow(vert.z, 2));
  vert.x = vert.x / mag;
  vert.y = vert.y / mag;
  vert.z = vert.z / mag;
}
vec3 cross (const vec3 & a, const vec3 & b)
{
  vec3 res{};
  res.x=a.y*b.z-a.z*b.y;
  res.y = a.z*b.x-a.x*b.z;
  res.z = a.x*b.y-a.y*b.x;
  return res;
}
void operator+=(vec3 & a, const vec3 & b)
{
  a.x+=b.x;
  a.y+=b.y;
  a.z+=b.z;
}
void calc_mesh_normals(vec3 *normals, const vec3 *verts, const int *faces, int nverts, int nfaces)
{
  for (int i = 0; i < nverts; i++)
  {
    normals[i] = {0, 0, 0};
  }
  for (int j = 1; j < nfaces-1; j++)
  {
  auto p = cross(verts[faces[j-1]],verts[faces[j+1]]);
  normals[faces[j-1]]+=p;
  normals[faces[j]]+=p;
  normals[faces[j+1]]+=p;
  }
  for(int i = 0; i < nverts; i++)
  {
    normalize(normals[i]);
  }
}

int main()
{
}