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<iostream>
#include<cstdio>
#define MN 100000
using namespace std;
inline int read()
{
	int x=0,f=1;char ch=getchar();
	while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
	while(ch>='0'&&ch<='9'){x=x*10+ch-'0';ch=getchar();}
	return x*f;
}
long long ans=0;
int n,m,head[MN+5],cnt=1,back[MN+5],flag=0,totv,tote,vis[MN+5],c[MN+5],num[3];
struct edge{int to,next;}e[MN*2+5];
inline void ins(int*head,int f,int t){e[++cnt]=(edge){t,head[f]};head[f]=cnt;}
void dfs(int x)
{
	++totv;++num[c[x]];vis[x]=1;
	for(int i=head[x];i;i=e[i].next)
		if(++tote,!vis[e[i].to]) c[e[i].to]=(c[x]+1)%3,dfs(e[i].to);
		else if(c[e[i].to]!=(c[x]+1)%3) flag=0;
	for(int i=back[x];i;i=e[i].next)
		if(!vis[e[i].to]) c[e[i].to]=(c[x]+2)%3,dfs(e[i].to);
		else if(c[e[i].to]!=(c[x]+2)%3) flag=0; 
}
int main()
{
	n=read();m=read();
	for(int i=1,j,k;i<=m;++i) j=read(),k=read(),ins(head,j,k),ins(back,k,j);
	for(int i=1;i<=n;++i) if(!vis[i]) 
	{
		totv=tote=0;flag=1;num[0]=num[1]=num[2]=0;
		dfs(i);
		if(flag&&num[0]&&num[1]&&num[2]) ans+=1LL*num[0]*num[1]+1LL*num[1]*num[2]+1LL*num[2]*num[0];
		else if(flag) ans+=tote;
		else ans+=totv+1LL*totv*(totv-1);
	}
	cout<<ans;
	return 0;
}