Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

The problem statement has recently been changed. View the changes.

×
B. Planets

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputGoa'uld Apophis captured Jack O'Neill's team again! Jack himself was able to escape, but by that time Apophis's ship had already jumped to hyperspace. But Jack knows on what planet will Apophis land. In order to save his friends, Jack must repeatedly go through stargates to get to this planet.

Overall the galaxy has *n* planets, indexed with numbers from 1 to *n*. Jack is on the planet with index 1, and Apophis will land on the planet with index *n*. Jack can move between some pairs of planets through stargates (he can move in both directions); the transfer takes a positive, and, perhaps, for different pairs of planets unequal number of seconds. Jack begins his journey at time 0.

It can be that other travellers are arriving to the planet where Jack is currently located. In this case, Jack has to wait for exactly 1 second before he can use the stargate. That is, if at time *t* another traveller arrives to the planet, Jack can only pass through the stargate at time *t* + 1, unless there are more travellers arriving at time *t* + 1 to the same planet.

Knowing the information about travel times between the planets, and the times when Jack would not be able to use the stargate on particular planets, determine the minimum time in which he can get to the planet with index *n*.

Input

The first line contains two space-separated integers: *n* (2 ≤ *n* ≤ 10^{5}), the number of planets in the galaxy, and *m* (0 ≤ *m* ≤ 10^{5}) — the number of pairs of planets between which Jack can travel using stargates. Then *m* lines follow, containing three integers each: the *i*-th line contains numbers of planets *a*_{i} and *b*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*, *a*_{i} ≠ *b*_{i}), which are connected through stargates, and the integer transfer time (in seconds) *c*_{i} (1 ≤ *c*_{i} ≤ 10^{4}) between these planets. It is guaranteed that between any pair of planets there is at most one stargate connection.

Then *n* lines follow: the *i*-th line contains an integer *k*_{i} (0 ≤ *k*_{i} ≤ 10^{5}) that denotes the number of moments of time when other travellers arrive to the planet with index *i*. Then *k*_{i} distinct space-separated integers *t*_{ij} (0 ≤ *t*_{ij} < 10^{9}) follow, sorted in ascending order. An integer *t*_{ij} means that at time *t*_{ij} (in seconds) another traveller arrives to the planet *i*. It is guaranteed that the sum of all *k*_{i} does not exceed 10^{5}.

Output

Print a single number — the least amount of time Jack needs to get from planet 1 to planet *n*. If Jack can't get to planet *n* in any amount of time, print number -1.

Examples

Input

4 6

1 2 2

1 3 3

1 4 8

2 3 4

2 4 5

3 4 3

0

1 3

2 3 4

0

Output

7

Input

3 1

1 2 3

0

1 3

0

Output

-1

Note

In the first sample Jack has three ways to go from planet 1. If he moves to planet 4 at once, he spends 8 seconds. If he transfers to planet 3, he spends 3 seconds, but as other travellers arrive to planet 3 at time 3 and 4, he can travel to planet 4 only at time 5, thus spending 8 seconds in total. But if Jack moves to planet 2, and then — to planet 4, then he spends a total of only 2 + 5 = 7 seconds.

In the second sample one can't get from planet 1 to planet 3 by moving through stargates.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/17/2021 20:13:06 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|