Making a Necklace

Changhyun was bothered by the many couples at school, so he decided to confess to Minjun, whom he had liked for a while.

Minjun likes material gifts, so Changhyun decided to make a necklace and give it to her as a present when he confesses. Changhyun has a necklace made of $N$ threads and $N$ beads. Number the beads from 1 to $N$ in some order. For every pair of integers $i$, $j$ with $1 \le i,j \le N$ and $i \equiv j \pm 1 \pmod{N}$, bead $i$ and bead $j$ are guaranteed to be connected by one thread. Minjun likes flashy gifts, so Changhyun decided to decorate the necklace with $M$ threads and $M$ beads.

First, Changhyun connects fewer than 30 beads with threads to make at most $N$ ornaments. An ornament has one more bead than it has threads. After making an ornament, Changhyun connects one bead of the ornament and one bead of the original necklace with a single thread. He repeats this until every ornament is attached to the original necklace. He does not attach two or more ornaments to the same bead, and he does not attach an ornament to a bead that was not part of the necklace before that ornament was attached.

The day of the confession finally came, and Changhyun brought the necklace to Minjun. But he then realized a big problem: Minjun was wearing a necklace identical to the one he had made. Changhyun immediately decided to make a new necklace.

Changhyun wants to check whether the new necklace is the same as the old one. Given two necklaces, write a program that determines whether they are the same.

Two decorated necklaces $A$ and $B$ are the same if the following holds. Number the beads of $A$ and $B$ appropriately. For any two numbers $1 \le x, y \le N+M$ with $x \neq y$, bead $x$ and bead $y$ are connected by one thread in $A$ if and only if bead $x$ and bead $y$ are connected by one thread in $B$.

The first line contains $N$ and $M$, separated by a space.

From the second line onward, the next $N+M$ lines each contain $u_i$ and $v_i$, in that order. This means that bead $u_i$ and bead $v_i$ are connected by a thread in the old necklace.

From line $N+M+2$ onward, the next $N+M$ lines each contain $x_j$ and $y_j$, in that order. This means that bead $x_j$ and bead $y_j$ are connected by a thread in the new necklace.

If the two necklaces are different, print Go to Minjun. If they are the same, print Retry.

$3 \le N \le 10^5$

$0 \le M \le \min(10^5, 29N)$

$1 \le u_i, v_i, x_j, y_j \le N+M$

The time limit is 1000 ms and the memory limit is 1024 MB.