Before revision:  Furthermore, we show when f's image is distributed (semi)symmetrically on }{\cal  {\rm  })}(}{\cal   = o(v _{\pi} ), and we identify two cases to demonstrate it.
After revision:  Furthermore, we show when f's image is distributed (semi)symmetrically on }{\cal {\rm trv })}(}{\cal = o(v _{\pi} ), and we identify two cases to demonstrate it.