A dollar sign is formed by drawing two parallel vertical lines through the letter $\mathrm{S}$, as shown. These lines cut the letter $S$ into 7 pieces. What is the minimum total number of parallel vertical lines that are needed to cut the letter S into exactly 154 pieces?
(A) 23
(B) 44
(C) 22
(D) 51
(E) 70

![](https://cdn.mathpix.com/cropped/2024_04_20_6027bc27089ed4fc493cg-061.jpg?height=371&width=144&top_left_y=682&top_left_x=1443)