B. Longtail Hedgehog

B. Longtail Hedgehog

time limit per test

3 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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.

Input

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.

Output

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

Sample test(s)

Input

8 6
4 5
3 5
2 5
1 2
2 8
6 7

Output

9

Input

4 6
1 2
1 3
1 4
2 3
2 4
3 4

Output

12

Note

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.

题意：在一幅图里面有从1到n个点，其中有m条线段。 Masha 想画一条刺猬的尾巴。求尾巴的终点的刺与尾巴长度的最大值。

解法：尾巴的的节点是连续递增的，从第一个点到n个点枚举，从前一个的状态依次递推出当期尾巴的长度，然后乘以刺的个数。

代码：

//#define zhouV
#include<string.h>
#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<vector> 
using namespace std;
#define LL __int64
#define maxn 1000010
LL len[maxn];
vector<LL>map[maxn];
int main() 
{
#ifdef zhouV
freopen("in.txt","r",stdin);
// freopen("out.txt","w",stdout);
#endif
LL n,m,u,v,res=0;
scanf("%I64d%I64d",&n,&m);
for(int i=0;i<m;i++)
{
scanf("%I64d%I64d",&u,&v);
map[u].push_back(v);
map[v].push_back(u);
}
for(int i=0;i<=n;i++)
{
len[i]=1;
}
  for(int i=1;i<=n;i++)
  {
  int sz=map[i].size();
  for(int j=0;j<sz;j++)
  {
  if(map[i][j]<i)
  {
  len[i]=max(len[i],len[map[i][j]]+1);
 }
 }
 if(res<len[i]*sz)
 {
  res=len[i]*sz;
 }
 }
 cout<<res<<endl;
    return 0;  

}