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>
using namespace std;
struct var{
	int to,nxt,c;
}edge[201001];
int n,m,x,y,cnt,head[101001],e,c[3],col[101001],t,num;
bool vis[101001];
long long ans;
void add(int u,int v,int c)
{
	cnt++;
	edge[cnt].to=v;
	edge[cnt].nxt=head[u];
	edge[cnt].c=c;
	head[u]=cnt;
}
int should(int o,int f)
{
	if(f==0)return (o+1)%3;
	else return (o-1+3)%3;
}
void dfs(int o)
{
	num++;
	for(int i=head[o];i;i=edge[i].nxt)
	{
		if(!edge[i].c)e++;
		int v=edge[i].to;
		if(col[v]!=-1)
		{
			if(col[v]!=should(col[o],edge[i].c))
			{
				t=-1;
			}
		}else
		{
			col[v]=should(col[o],edge[i].c);
			if(t!=-1&&!c[col[v]])t++;
			c[col[v]]++;
			dfs(v);
		}
	}
}
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		scanf("%d%d",&x,&y);
		add(x,y,0);
		add(y,x,1);
	}
	memset(col,-1,sizeof(col));
	for(int i=1;i<=n;i++)
	{
		if(col[i]!=-1)continue;
		c[0]=1,c[1]=c[2]=0;
		col[i]=0;
		vis[i]=1;
		e=0;
		t=1;
		num=0;
		dfs(i);
		if(t==-1)ans+=1ll*num*num;
		else if(t<3)ans+=1ll*e;
		else ans+=1ll*c[0]*c[1]+1ll*c[0]*c[2]+1ll*c[1]*c[2];
	}
	printf("%lld",ans);
}