CF615B.Longtail Hedgehog

This Christmas Santa gave Masha a magic picture and a pencil. The picture consists of n points connected by m segments (they might cross in any way, that doesn't matter). No two segments connect the same pair of points, and no segment connects the point to itself. Masha wants to color some segments in order paint a hedgehog. In Mashas mind every hedgehog consists of a tail and some spines. She wants to paint the tail that satisfies the following conditions:

1. Only segments already presented on the picture can be painted;
2. The tail should be continuous, i.e. consists of some sequence of points, such that every two neighbouring points are connected by a colored segment;
3. The numbers of points from the beginning of the tail to the end should strictly increase.

Masha defines the length of the tail as the number of points in it. Also, she wants to paint some spines. To do so, Masha will paint all the segments, such that one of their ends is the endpoint of the tail. Masha defines the beauty of a hedgehog as the length of the tail multiplied by the number of spines. Masha wants to color the most beautiful hedgehog. Help her calculate what result she may hope to get.

Note that according to Masha's definition of a hedgehog, one segment may simultaneously serve as a spine and a part of the tail (she is a little girl after all). Take a look at the picture for further clarifications.

今年圣诞节，圣诞老人送给玛莎一幅魔法画和一支铅笔。这幅画由 $n$ 个点和 $m$ 条线段组成（这些线段可以以任意方式相交，这无关紧要）。不存在连接相同一对点的两条不同线段，也不存在连接某点与其自身的线段。玛莎希望给其中一些线段涂色，从而画出一只刺猬。在玛莎心中，每只刺猬都由一条“尾巴”和若干“尖刺”组成。她希望将尾巴涂色，并满足以下条件：

1. 只能涂画中已有的线段；
2. 尾巴必须是连续的，即由某个点序列构成，使得序列中每两个相邻点之间都有一条被涂色的线段相连；
3. 尾巴从起点到终点的点的编号必须严格递增。

玛莎将尾巴的长度定义为其中所含点的个数。此外，她还希望涂出若干尖刺：她会将所有一端为尾巴终点的线段全部涂色。玛莎将刺猬的“美丽值”定义为：尾巴长度 × 尖刺数量。玛莎希望涂出最美丽的刺猬。请帮她计算她所能达到的最大美丽值。

注意：根据玛莎对刺猬的定义，同一条线段可能同时作为尖刺和尾巴的一部分（毕竟她只是个小女孩）。请参看图片以获得进一步说明。

First line of the input contains two integers n and m(2 ≤ n ≤ 100 000, 1 ≤ m ≤ 200 000) — the number of points and the number segments on the picture respectively.

Then follow m lines, each containing two integers u__i and v__i (1 ≤ u__i, v__i ≤ n, u__i ≠ v__i) — the numbers of points connected by corresponding segment. It's guaranteed that no two segments connect the same pair of points.

输入的第一行包含两个整数 $n$ 和 $m$（$2 \leq n \leq 100\,000$，$1 \leq m \leq 200\,000$）—— 分别表示图中点的数量和线段的数量。

接下来是 $m$ 行，每行包含两个整数 $u_i$ 和 $v_i$（$1 \leq u_i,\,v_i \leq n$，$u_i \neq v_i$）—— 表示由对应线段连接的两个点的编号。保证不存在两条线段连接同一对点。

Print the maximum possible value of the hedgehog's beauty.

输出刺猬美观度的最大可能值。

The picture below corresponds to the first sample. Segments that form the hedgehog are painted red. The tail consists of a sequence of points with numbers 1, 2 and 5. The following segments are spines: (2, 5), (3, 5) and (4, 5). Therefore, the beauty of the hedgehog is equal to 3·3 = 9.

下图对应第一个样例。构成刺猬的线段被涂成红色。尾巴由编号为 1、2 和 5 的点组成的序列构成。以下线段为刺：(2, 5)、(3, 5) 和 (4, 5)。因此，该刺猬的美观度等于 $3 \cdot 3 = 9$。