Shelter

City A has $N$ buildings. The buildings are connected by $N-1$ bidirectional roads, and there is exactly one path between every pair of buildings.

Each road has a travel time. If a road connects buildings $u$ and $v$ and has travel time $w$, traveling along that road takes $w$ units of time in either direction.

A huge meteorite is expected to fall into the sea near City A and cause a tsunami. To help citizens evacuate as quickly as possible, the mayor, Atli, will choose exactly one building and construct a shelter there.

If the shelter is built at building $i$, let $C_i$ be the maximum shortest-path travel time from building $i$ to any building. In other words, $C_i$ is the travel time from the shelter to the farthest building.

Atli wants to choose the shelter location so that $C_i$ is minimized.

Find the minimum possible value of $C_i$ and the number of a building that achieves it. If several buildings achieve the same minimum value, print the smallest building number.

The input is given in the following format:

$N$ $u_1\ v_1\ w_1$

Print the minimum possible shelter cost on the first line.

On the second line, print the number of a building that achieves this cost. If several buildings do so, print the smallest building number.

• $1 \leq N \leq 200\,000$.
• $1 \leq u_i,v_i \leq N$ ().