Hi can someone help me figure out an algorithm to solve this problem? I know the answer is 141 but not sure how

Spiders web A spider sits at the bottom (point S) of its web, and a fly sits at the top (F). How many different ways can the spider reach the fly by moving along the webs lines in the directions indicated by the arrows? [Kor05]

https://encrypted.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&ved=0ahUKEwierrDHxrPSAhUIaRQKHSelAEoQFgghMAE&url=http%3A%2F%2Fwww.vgloop.com%2F_files%2F1394454921-126688.pdf&usg=AFQjCNHo2kvnKW_R3U5aS5ynuaqqv_l_cg&sig2=dryyLDdkecWEkbZryZYTnA

for some reason i am having difficulty posting a picture of the question but that is the link to the book and it is number 10 in section 4.2 excercies .