Longtail Hedgehog

Description

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 ui and vi (1 ≤ ui, vi ≤ n, ui ≠ vi) — 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 Input

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
      

Hint

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.

這道題需要求尾巴長度*刺的個數最大值，尾巴需要遞增，刺是沒有要求的，

就算尾巴和刺是同一個也沒用關系。

隻是處理不能用圖來處理，直接對小的邊排序，那麼就可以求出，以某點

結尾的最長遞增長度*與此點連接配接邊的個數。

#include <stdio.h>
#include <string.h>
#include <algorithm>
#define LL long long
const int maxn = 100005;
int l[maxn], cnt[maxn];
struct node
{
    int u, v;
    node ( ) { }
    node ( int a, int b ) { u = a, v = b; }
    friend bool operator < ( node n1, node n2 )
    {
        return n1.u < n2.u;
    }
}a[maxn*4];
inline int Max ( int a, int b ) { return a > b ? a : b; }
int main ( )
{
    int n, m, u, v, pos = 0;
    LL ans = 0;
    scanf ( "%d%d", &n, &m );
    while ( m -- )
    {
        scanf ( "%d%d", &u, &v );
        if ( u > v ) //因為要求的是遞增的序列,是以讓小的在前面
        {
            int t = u;
            u = v;
            v = t;
        }
        cnt[v] ++;  //刺的個數(即與其相連的邊的個數)
        cnt[u] ++;
        a[pos ++] = node ( u, v );
    }
    std :: sort ( a, a+pos );   //對第一個數排序,那樣就可以求出尾巴的長度
    for ( int i = 0; i < pos; i ++ )
    {
        u = a[i].u, v = a[i].v;
        l[u] = Max ( l[u], 1 ); //小的有可能為0
        l[v] = Max ( l[v], l[u]+1 );    //直接等于小的+1或本身的個數
    }
    for ( int i = 1; i <= n; i ++ )
    {
        LL val = ( LL )l[i]*cnt[i];
        if ( ans < val )
            ans = val;
    }
    printf ( "%lld\n", ans );
    return 0;
}