There is a tree with $n$ vertices. There are also $m$ ants living on it. Each ant has its own color. The $i$-th ant has two favorite pairs of vertices: ($a_i, b_i$) and ($c_i, d_i$). You need to tell if it is possible to paint the edges of the tree in $m$ colors so that every ant will be able to walk between vertices from one of its favorite pairs using only edges of his color; if it is possible, you need to print which pair every ant should use.
The first line contains a single integer $n$ ($2 \leq n \leq 10^5$) — the number of vertices.

Each of the next $n-1$ lines contains two integers $u_i$ and $v_i$ ($1 \leq u_i, v_i \leq n$), meaning that there is an edge between vertices $u_i$ and $v_i$.

The next line contains a single integer $m$ ($1 \leq m \leq 10^4$) — the number of ants.

Each of the next $m$ lines contains four integers $a_i$, $b_i$, $c_i$, and $d_i$ ($1 \leq a_i, b_i, c_i, d_i \leq n$, $a_i \neq b_i, c_i \neq d_i$), meaning that pairs ($a_i$, $b_i$) and ($c_i$, $d_i$) are favorite for the $i$-th ant.
print("_RANDOM_GUESS_1689631942.387503")# 1689631942.3875234