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D. Ants
time limit per test
3 seconds
memory limit per test
768 megabytes
input
standard input
output
standard output

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.

Input

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.

Output

Print "NO" (without quotes) if the wanted painting is impossible.

Otherwise, print "YES" (without quotes). Print $m$ lines. On the $i$-th line, print $1$ if the $i$-th ant will use the first pair and $2$ otherwise. If there are multiple answers, print any.

Examples
Input
61 23 14 15 26 232 6 3 41 6 6 51 4 5 2
Output
YES212
Input
51 21 31 41 522 3 4 53 4 5 2
Output
NO
Note

In the sample, the second and the third edge should be painted in the first color, the first and the fifth should be painted in the second color, and the fourth should be painted in the third color.