[USACO07MAR] Cow Traffic S

The bovine population boom down on the farm has caused serious congestion on the cow trails leading to the barn. Farmer John has decided to conduct a study to find the bottlenecks in order to relieve the 'traffic jams' at milking time. The pasture contains a network of M (1 ≤ M ≤ 50,000) one-way trails, each of which connects exactly two different intersections from the set of N (1 ≤ N ≤ 5,000) intersections conveniently numbered 1..N; the barn is at intersection number N. Each trail connects one intersection point to another intersection point with a higher number. As a result, there are no cycles and, as they say on the farm, all trails lead to the barn. A pair of intersection points might be connected by more than one trail. During milking time rush hour, the cows start from their respective grazing locations and head to the barn. The grazing locations are exactly those intersection points with no trails connecting into them. Each cow traverses a 'path', which is defined as a sequence of trails from a grazing location to the barn. Help FJ finding the busiest trail(s) by computing the largest number of possible paths that contain any one trail. The answer is guaranteed to fit in a signed 32-bit integer. 随着牛的数量增加，农场的道路的拥挤现象十分严重，特别是在每天晚上的挤奶时间。为了解决这个问题，FJ决定研究这个问题，以能找到导致拥堵现象的瓶颈所在。 牧场共有M条单向道路，每条道路连接着两个不同的交叉路口，为了方便研究，FJ将这些交叉路口编号为1..N,而牛圈位于交叉路口N。任意一条单向道路的方向一定是是从编号低的路口到编号高的路口，因此农场中不会有环型路径。同时，可能存在某两个交叉路口不止一条单向道路径连接的情况。 在挤奶时间到来的时候，奶牛们开始从各自的放牧地点回到牛圈。放牧地点是指那些没有道路连接进来的路口（入度为0的顶点）。 现在请你帮助fj通过计算从放牧点到达牛圈的路径数目来找到最繁忙的道路（答案保证是不超过32位整数）。

Line 1: Two space-separated integers: N and M. Lines 2..M+1: Two space-separated intersection points.

Line 1: The maximum number of paths passing through any one trail.

7 7
1 3
3 4
3 5
4 6
2 3
5 6
6 7

4

Here are the four possible paths that lead to the barn: 1 3 4 6 7 1 3 5 6 7 2 3 4 6 7 2 3 5 6 7