Codeforces 602C The Two Routes【最短路+思维】

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 2
1 3
1 4
2 3
2 4
3 4

output

-1

input

5 5
4 2
3 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.

题目大意：

有n个城市，m条火车路，对于一个完全图来讲，如果这条路上要么建的是火车路 ，要么是正常路，火车路走火车，正常路走汽车。就是说，对于map【i】【j】，这条路要么是火车路，要么是正常路，问在不走重复城市的情况下（起点终点不算），两个人同时在城市1出发，目标是城市n，问最后到达的那个人走的最小路程，每条路长度为1.

思路：

1、对于完全图，map【1】【n】这条边，要么是火车路，要么是汽车路，如果是火车路，我们就求汽车路的最短路，如果是汽车路，我们就求火车路的最短路。

2、那么如果map【1】【n】==0，将图取反，跑Floyd（数据不大，取最优代码量）；

Ac代码：

#include
#include
#include
using namespace std;
int map[500][500];
int main()
{
    int n,m;
    while(~scanf("%d%d",&n,&m))
    {
        memset(map,0,sizeof(map));
        for(int i=0;i