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;
const int N=1e5+5;
int col[N];
int Head[N],Next[N<<1],Adj[N<<1],Weight[N<<1],tot=0;
void addedge(int u,int v,int w){
	Next[++tot]=Head[u],Head[u]=tot,Adj[tot]=v,Weight[tot]=w;
}
int calc(int x){
	if (x<=0) return x+3;
	if (x>3) return x-3;
	return x;
} 
int sz=0,E=0,cnt[5];bool flag=true;
void dfs(int x){
	sz++,cnt[col[x]]++;
	for (int e=Head[x];e;e=Next[e]){
		if (!col[Adj[e]]) {
			col[Adj[e]]=calc(col[x]+Weight[e]);
			dfs(Adj[e]);
		}else{
			if (col[Adj[e]]==calc(col[x]+Weight[e])) continue;
			else flag=false;
		}
	}
}
int main (){
	int n,m;scanf ("%d%d",&n,&m);
	for (int i=1;i<=m;i++){
		int u,v;scanf ("%d%d",&u,&v);
		addedge(u,v,1);
		addedge(v,u,-1);
	}
	long long ans=0;
	for (int i=1;i<=n;i++)
		if (!col[i]) {
			cnt[1]=cnt[2]=cnt[3]=sz=0;
			col[i]=1;flag=true;E=0;
			dfs(i);
			if (!flag) ans+=1ll*sz*sz;
			else if (cnt[1]&&cnt[2]&&cnt[3]) ans+=1ll*cnt[1]*cnt[2]+1ll*cnt[2]*cnt[3]+1ll*cnt[1]*cnt[3];
			else ans+=sz-1;
		}
	printf ("%lld",max(ans,1ll*m));
	return 0;
}