#P690F3. Tree of Life (hard)

Tree of Life (hard)

Description

To add insult to injury, the zombies have taken all but two drawings from Heidi! Please help her recover the Tree of Life from only these two drawings.

The input format is the same as in the medium version, except that now the bound on n is 2 ≤ n ≤ 1000 and that k = 2.

The same as in the medium version.

Input

The input format is the same as in the medium version, except that now the bound on n is 2 ≤ n ≤ 1000 and that k = 2.

Output

The same as in the medium version.

Samples

1
9 2
6
4 3
5 4
6 1
8 6
8 2
7 1
5
8 6
8 7
8 1
7 3
5 1

YES
2 1
3 1
5 4
6 5
7 6
8 5
9 8
1 4