Codeforces Round #333 (Div. 2) C. The Two Routes

C. The Two Routes

time limit per test
2 seconds

memory limit per test
256 megabytes

input
standard input

output
standard output

In Absurdistan, there are n towns (numbered 1 through n)
and m bidirectional railways. There is also an absurdly simple road network — for each pair of different towns x and y,
there is a bidirectional road between towns x and y if
and only if there is no railway between them. Travelling to a different town using one railway or one road always takes exactly one hour.

A train and a bus leave town 1 at the same time. They both have the same destination, town n,
and don't make any stops on the way (but they can wait in town n). The train can move only along railways and the bus can move only
along roads.

You've been asked to plan out routes for the vehicles; each route can use any road/railway multiple times. One of the most important aspects to consider is safety — in order to avoid accidents at railway crossings, the train and the bus must not arrive at the
same town (except town n) simultaneously.

Under these constraints, what is the minimum number of hours needed for both vehicles to reach town n (the maximum of arrival times
of the bus and the train)? Note, that bus and train are not required to arrive to the town n at the same moment of time, but are allowed
to do so.

Input

The first line of the input contains two integers n and m (2 ≤ n ≤ 400, 0 ≤ m ≤ n(n - 1) / 2) —
the number of towns and the number of railways respectively.

Each of the next m lines contains two integers u and v,
denoting a railway between towns u and v (1 ≤ u, v ≤ n, u ≠ v).

You may assume that there is at most one railway connecting any two towns.

Output

Output one integer — the smallest possible time of the later vehicle's arrival in town n. If it's impossible for at least one of the
vehicles to reach town n, output  - 1.

Sample test(s)

input

4 2
1 3
3 4

output

2

input

4 6
1 21 31 4
2 32 4
3 4

output

-1

input

5 5
4 23 5
4 5
5 1
1 2

output

3

Note

In the first sample, the train can take the route

and
the bus can take the route

.
Note that they can arrive at town 4 at the same time.

In the second sample, Absurdistan is ruled by railwaymen. There are no roads, so there's no way for the bus to reach town 4.

题意：有n个城市有m条铁路，有铁路就没有公路(没有铁路的地方有公路)。求从1到n，A走铁路的最短时间x，B走公路的最短时间y（中间不能停但是可以在n点等，A和B不能再中间相遇，n点除外)，求A和B在n点相遇是的最短时间。
坑爹的题意，看了我半天。
1直接到n如果没有公路就有铁路(关键)，所以不要被题目迷惑了，这样就不用考虑中间相遇的问题了。
就是一个最短路径的问题了。
还是太浮躁了没有好好分析题目。