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<bits/stdc++.h>
const int N=1e5+5;
int n,m,a[N],b[N],i,id[N],od[N],g[N*3],s1[N*3],s2[N*3];
bool bb[N*3];
int gfa(int x){
	return g[x]==x?x:g[x]=gfa(g[x]);
}
inline void uni(int x,int y){
	g[gfa(x)]=gfa(y);
}
int main(){
	scanf("%d%d",&n,&m);for(i=1;i<=n*3;++i)g[i]=i;
	for(i=1;i<=m;++i)scanf("%d%d",a+i,b+i),++od[a[i]],++id[b[i]],
		uni(a[i],b[i]+n),uni(a[i]+n,b[i]+n*2),uni(a[i]+n*2,b[i]);
	for(i=1;i<=n;++i){
		++s1[gfa(i)],++s2[gfa(i+n)];
		if(id[i] && od[i])bb[gfa(i)]=bb[gfa(i+n)]=bb[gfa(i+n*2)]=1;
	}
	long long ans=0;
	for(i=1;i<=n*3;++i)if(gfa(i)==i && bb[i])ans+=1ll*s1[i]*s2[i];
	for(i=1;i<=m;++i)ans+=!bb[gfa(a[i])];
	printf("%lld\n",ans);
	return 0;
}