Bus Routes

The bus lines of a city are known. Every line is a list of stops, and its buses drive the route in both directions - so once you are on a bus you may get off at any other stop of that same line. One such trip is called a ride, and changing to another bus starts a new ride.

Your task is to find the smallest number of rides needed to travel from a given starting stop to a given final stop.

Input

First line of input will be a single integer $t$ - the number of testcases.
First line of each testcase contains two integers $s$ and $n$ - the number of stops in the city and the number of bus lines. The stops are numbered $1$ to $s$.
In the next $n$ lines will be one bus line each: first the number $m$ of stops on its route, and then $m$ distinct stop numbers.
Last line of the testcase contains two integers $a$ and $b$ - the starting and the final stop.

Output

For every testcase print a single line with the smallest number of rides needed to get from stop $a$ to stop $b$. If it cannot be done, print $-1$. If $a$ and $b$ are the same stop the answer is $0$, since no ride is needed.

Example

1
7 2
3 1 2 7
3 3 6 7
1 6

2

Board the first bus at stop $1$ and stay on it until stop $7$, then change to the second bus, which carries you to stop $6$. Two rides, and there is no way to do it in one - no single line holds both stop $1$ and stop $6$.

Constraints

$1\le t\le 1000$
$1\le s\le 10^5$
$1\le n\le 10^5$
$1\le m$
$1\le a,b\le s$
the stops listed for one bus line are distinct
the sum of $s$ over all testcases does not exceed $2\cdot 10^5$
the sum of all $m$ over all testcases does not exceed $2\cdot 10^5$

This problem was adapted, with permission, from Autobuske rute, authored by Društvo matematičara Srbije and Fondacija Petlja.