2 - Reach a level

You are playing a computer game. This game has $n$ levels numbered with the integers from $1$ to $n$. At any point in time, you are located at one of the levels with some **penalty**, represented by a non-negative real number. Initially, you start at level $1$ with penalty $0$. There are $m$ options to change levels. Each option is described by pair of levels $s$, $f$ (possibly equal) and penalty