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>
#define ll long long
#define rep(i,j,k) for (i=j;i<=k;i++)
using namespace std;
const int N=1e5+5;
int n,m,i,u,v,tot,flg,E;
int En,fst[N],to[N*2],sgn[N*2],nxt[N*2],vis[N],cnt[3],col[N];
ll ans;
void add(int u,int v,int SGN) {
	En++; nxt[En]=fst[u]; fst[u]=En; to[En]=v; sgn[En]=SGN;
}
int inc(int x) {return (x+1)%3;}
int dec(int x) {return (x+2)%3;}
void dfs(int x)
{
	int j,v,dc;
	vis[x]=1; tot++; cnt[col[x]]++;
	for (j=fst[x];j;j=nxt[j])
	{
		E++;
		if (sgn[j]==1) dc=inc(col[x]);
		else dc=dec(col[x]);
		v=to[j];
		if (vis[v]) {
			if (dc!=col[v]) flg=1;
		}
		else {
			col[v]=dc;
			dfs(v);
		}
	}
}
int main()
{
//	freopen("blackout.in","r",stdin);
//	freopen("blackout.out","w",stdout);
	scanf("%d%d",&n,&m);
	rep(i,1,m)
	{
		scanf("%d%d",&u,&v);
		add(u,v,1); add(v,u,-1);
	}
	rep(i,1,n)
		if (!vis[i])
		{
			flg=tot=E=0; cnt[0]=cnt[1]=cnt[2]=0;
			dfs(i); E/=2;
			if (flg) ans+=(ll)tot*tot;
			else if (cnt[0] && cnt[1] && cnt[2]) ans+=(ll)cnt[0]*cnt[1]+(ll)cnt[1]*cnt[2]+(ll)cnt[2]*cnt[0];
			else ans+=E;
		}
	printf("%lld\n",ans);
	return 0;
}