Cowherd and Weaver Girl

Cowherd lives in a weighted undirected tree $E$ with $N$ vertices, and Weaver Girl lives in a weighted undirected tree $W$ with $M$ vertices.

The two live in different trees, so they cannot meet. To help the two lovers, the Jade Emperor builds a magpie bridge every year on July 7 so they can meet.

The magpie bridge is an edge of length $1$. The Jade Emperor connects it so that the sum of distances between all vertices of $E$ and all vertices of $W$ is minimized, which makes it easy for the two to meet.

Tell them which vertices the bridge connects on July 7.

The first line contains $N$, the number of vertices in $E$ ($1 \leq N \leq 100\,000$). The next $N-1$ lines each describe an edge of $E$ in the form a b c $(1 \leq a, b \leq N; 1 \leq c \leq 10^4)$. This means the distance between vertex $a$ and vertex $b$ of $E$ is $c$. The next line contains $M$, the number of vertices in $W$ ($1 \leq M \leq 100\,000$). The next $M-1$ lines each describe an edge of $W$ in the form a b c $(1 \leq a, b \leq M; 1 \leq c \leq 10^4)$. This means the distance between vertex $a$ and vertex $b$ of $W$ is $c$. All input values are integers.

The first line prints the vertex of $E$ and the vertex of $W$ that the bridge connects, separated by a space. If several answers exist, print any of them. The second line prints the sum of distances between all vertices of $E$ and all vertices of $W$ after the bridge is built.

The sum of distances between all vertices of $E$ and all vertices of $W$ is defined as follows. $\sum_{u \in E} \sum_{v \in W} dist(u, v)$