Problem: We have a grid with N rows and N columns. The cell at the i-th row and j-th column is denoted (i, j).

Initially, M of the cells are painted black, and all other cells are white. Specifically, the cells (a_1, b_1), (a_2, b_2), ..., (a_M, b_M) are painted black.

Snuke will try to paint as many white cells black as possible, according to the following rule:

* If two cells (x, y) and (y, z) are both black and a cell (z, x) is white for integers 1≤x,y,z≤N, paint the cell (z, x) black.



Find the number of black cells when no more white cells can be painted black.

Constraints

* 1≤N≤10^5
* 1≤M≤10^5
* 1≤a_i,b_i≤N
* All pairs (a_i, b_i) are distinct.

Input

The input is given from Standard Input in the following format:


N M
a_1 b_1
a_2 b_2
:
a_M b_M


Output

Print the number of black cells when no more white cells can be painted black.

Examples

Input

3 2
1 2
2 3


Output

3


Input

2 2
1 1
1 2


Output

4


Input

4 3
1 2
1 3
4 4


Output

3

Solution (in CPP):

Solution:
#include<cstdio>
#include<numeric>
using i64=long long;
const int N=300007;
int a[N],b[N],f[N],g[N],fa[N],s[N],t[N],vis[N];
int read(){int x;scanf("%d",&x);return x;}
int find(int x){return x==fa[x]? x:fa[x]=find(fa[x]);}
void merge(int x,int y){fa[find(x)]=find(y);}
int main()
{
    int n=read(),m=read();i64 ans=0;std::iota(fa+1,fa+n*3+1,1);
    for(int i=1;i<=m;++i) ++f[a[i]=read()],++g[b[i]=read()],merge(a[i],b[i]+n),merge(a[i]+n,b[i]+n+n),merge(a[i]+n+n,b[i]);
    for(int i=1;i<=n;++i) if(++s[find(i)],++t[find(i+n)],f[i]&&g[i]) vis[find(i)]=vis[find(i+n)]=vis[find(i+n+n)]=1;
    for(int i=1;i<=n*3;++i) if(find(i)==i&&vis[i]) ans+=1ll*s[i]*t[i];
    for(int i=1;i<=m;++i) ans+=!vis[find(a[i])];
    printf("%lld\n",ans);
}