Yanggallae Rescue

The peaceful village of Yanggallae is in danger! Poison is spreading through the vines and moving toward the room where Yanggallae is.

The poison spreads from every room except room 1 that is connected to exactly one vine.

There is exactly one path between any pair of rooms, and there are $N-1$ vines in total. Each end of a vine is strongly attached to its room, so the vines must be cut to keep the poison from reaching the room where Yanggallae is.

Cutting a vine takes effort equal to its thickness $V$. Shiyeon wants to cut the vines using as little total effort as possible.

Find the minimum total effort needed to cut the vines.

The first line contains the number of rooms $N$. ($2 \leq N \leq 100\,000$)

Each of the next $N-1$ lines contains three integers $A$, $B$, and $V$. ($1 \leq A, B \leq N$, $1 \leq V \leq 1\,000$)

This means the vine connecting room $A$ and room $B$ has thickness $V$.

The room where Yanggallae is tied is numbered $1$.

Print the minimum total effort needed to cut the vines.

In the figure, cutting the vine between 1 and 2, the vine between 3 and 6, and the vine between 3 and 7 gives the minimum total of 3+1+2 = 6.