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;
template<typename T>inline T read(){
	T f=0,x=0;char c=getchar();
	while(!isdigit(c)) f=c=='-',c=getchar();
	while(isdigit(c)) x=x*10+c-48,c=getchar();
	return f?-x:x;
}
namespace run{
	const int N=4e5+9;
	int head[N],nex[N],to[N],w[N],cnt;
	inline void add(int u,int v,int c){
		nex[++cnt]=head[u];
		head[u]=cnt,to[cnt]=v,w[cnt]=c;
	}

	int n,m,vis[N],tot,num[4],PC,cntm;
	inline void dfs(int u,int col){
		vis[u]=col,num[col]++,tot++;
		for(int i=head[u];i;i=nex[i]){
			if(!vis[to[i]]){
				dfs(to[i],(col+w[i]+2)%3+1);
			}else if(vis[to[i]]!=(col+w[i]+2)%3+1) PC=1;
			cntm+=w[i]==1;
		}
	}
	int main(){
		n=read<int>(),m=read<int>();
		for(int i=1;i<=m;i++){
			int u=read<int>(),v=read<int>();
			add(u,v,1),add(v,u,-1);
		}

		long long ans=0;
		for(int i=1;i<=n;i++) if(!vis[i]){
			num[3]=num[1]=num[2]=tot=cntm=PC=0,dfs(i,1);
			if(PC) ans+=1LL*tot*tot;
			else if(!num[3] || !num[1] || !num[2]) ans+=cntm;
			else ans+=1LL*num[3]*num[1]+1LL*num[3]*num[2]+1LL*num[1]*num[2];
		}
		printf("%lld\n",ans);
		return 0;
	}
}
int main(){
#ifdef my
	freopen("black.in","r",stdin);
	freopen("black.out","w",stdout);
#endif
	return run::main();
}