*American Mathematical Monthly*,

August-September 2012, about

**straight line programs**. The article,

by Peter Borwein and Joe Hobart, was about how these things would be

affected by allowing the division operation. But a rather simple idea

for a puzzle formed in my head after reading it. So, here it is:

A

**straight line program**is a sequence of integers p

_{1},p

_{2},p

_{3},....,p

_{n}

such that p

_{1}=1 and p

_{i}is the sum, difference, or product of p

_{k}and p

_{l}

where k and l are both less than i. It is OK if k=l. So, for example,

one possible straight line program which ends in 12 is 1,2,4,3,12. To be

explicit, p

_{1}=1, p

_{2}=p

_{1}+p

_{1}, p

_{3}=p

_{2}+p

_{2}, p

_{4}=p

_{3}-p

_{1}, p

_{5}=p

_{4}*p

_{3}.

Find a shortest straight line program ending in 137.