Apple Delivery

Bessie has two crisp red apples to deliver to two of her friends in the herd.

The pastures are numbered $1$ through $P$ ($1 \le P \le 100{,}000$) and are connected by $C$ bidirectional cowpaths ($1 \le C \le 200{,}000$). Each cowpath connects two distinct pastures $P1_i$ and $P2_i$ and has length $D_i$. No cowpath leads from a pasture to itself. The sum of all cowpath lengths $\sum D_i$ does not exceed $2{,}000{,}000{,}000$. It is always possible to travel from any pasture to any other pasture.

Bessie starts at pasture $PB$ and must deliver both apples by visiting the two distinct pastures $PA1$ and $PA2$ in either order. The three pastures $PB$, $PA1$, and $PA2$ are all distinct. She may reuse pastures and cowpaths she has already visited, and the distance traveled is the sum of the lengths of all cowpaths she uses.

Find the minimum total distance Bessie must travel to deliver both apples.

The map below illustrates pasture numbers (in brackets) together with the cowpaths and their lengths.

                3        2       2
           [1]-----[2]------[3]-----[4]
             \     / \              /
             7\   /4  \3           /2
               \ /     \          /
               [5]-----[6]------[7]
                    1       2

The first line contains five space-separated integers $C$, $P$, $PB$, $PA1$, and $PA2$.

Each of the next $C$ lines describes cowpath $i$ with three integers $P1_i$, $P2_i$, and $D_i$: the two pastures it connects and its length.

Print, on a single line, the minimum total distance Bessie must travel to deliver both apples.