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;
typedef long long LL;

const int N=1e5+10;

struct Edge{int to,next,cost; }way[N<<1];

int n,m,num[N],tot;
LL ans;

void Build(int a,int b,int cost) { way[++tot]=(Edge){b,num[a],cost}; num[a]=tot; }

void Init()
{
	scanf("%d%d",&n,&m);
	int a,b;
	for (int i=1;i<=m;++i)
	{
		scanf("%d%d",&a,&b);
		Build(a,b,1); Build(b,a,2);	
	}
}

int cnt[4],col[N],totedge;
bool circle;
void Dfs(int x)
{
	cnt[col[x]]++;
	for (int i=num[x];i;i=way[i].next)
	{
		int v=way[i].to,d=(col[x]+way[i].cost)%3;
		if (i&1) totedge++;
		if (col[v]==-1) col[v]=d,Dfs(v);
		else if (col[v]!=d) circle=1;
	}
}

void Solve()
{
	for (int i=1;i<=n;++i) col[i]=-1;
	
	LL ans=0;
	for (int i=1;i<=n;++i)
		if (col[i]==-1)
		{
			circle=0; totedge=0; col[i]=0; cnt[0]=cnt[1]=cnt[2]=0;
			Dfs(i);
			if (circle) ans+=1ll*(cnt[0]+cnt[1]+cnt[2])*(cnt[0]+cnt[1]+cnt[2]);
			else if (cnt[0] && cnt[1] && cnt[2]) ans+=1ll*cnt[0]*cnt[1]+1ll*cnt[1]*cnt[2]+1ll*cnt[2]*cnt[0];
			else ans+=totedge;
		}
	printf("%lld\n",ans);
}

int main()
{
	Init();
	Solve();
	return 0;
}