Road To Savings

Pat Wholes is in charge of road maintenance in Capitol City. The roads are in such poor shape that accidents happen almost every day, and the public is furious. Pat would like to pave every road in the city, but he also wants to keep his job. The mayor would replace him if the paving costs too much, so Pat must decide which roads to pave and which to leave alone. Since the mayor's happiness is the ultimate goal, Pat will pave only the roads that lie on a shortest path from the mayor's house to the mayor's office. Several equally short routes may exist, but many roads still lie on none of these paths, and Pat hopes that plenty of roads do not need paving. Pat came down to your basement cubicle to ask for the total length of the roads that do not need to be paved.

Four positive integers $n$ $m$ $a$ $b$ are given on the first line ($n, a, b \leq 100$, $a \neq b$). Here $n$ is the number of intersections in the town, numbered 1 to $n$, $m$ is the number of roads connecting the intersections, and $a$ and $b$ are the intersections where the mayor's house and office are located. Then $m$ lines follow, each containing three numbers $i_1$ $i_2$ $\ell$ ($1 \leq i_1, i_2 \leq n$, $i_1 \neq i_2$, $1 \leq \ell \leq 100$), meaning a two-way road exists between intersections $i_1$ and $i_2$ with length $\ell$. At most one road exists between any two intersections, and at least one path exists between $a$ and $b$.

Output the total length of all roads that do not need to be paved.