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:
// ====================================
//   author: M_sea
//   website: https://m-sea-blog.com/
// ====================================
#include <bits/stdc++.h>
using namespace std;
typedef long long ll;

int read() {
	int X=0,w=1; char c=getchar();
	while (c<'0'||c>'9') { if (c=='-') w=-1; c=getchar(); }
	while (c>='0'&&c<='9') X=X*10+c-'0',c=getchar();
	return X*w;
}

const int N=100000+10;

int n,m;

struct edge { int v,w,nxt; } e[N<<1];
int head[N];
void addEdge(int u,int v,int w) {
	static int cnt=0;
	e[++cnt]=(edge){v,w,head[u]},head[u]=cnt;
}

int szn,szm,flag;
int vis[N],col[N],cnt[3];
int nxt(int c,int w) { return (c+w+3)%3; }
void dfs(int u,int c) {
	vis[u]=1,col[u]=c,++cnt[c],++szn;
	for (int i=head[u];i;i=e[i].nxt) {
		int v=e[i].v,w=e[i].w;
		if (w==1) ++szm;
		if (!vis[v]) dfs(v,nxt(c,w));
		else if (col[v]!=nxt(c,w)) flag=1;
	}
}

int main() {
	n=read(),m=read();
	for (int i=1;i<=m;++i) {
		int u=read(),v=read();
		addEdge(u,v,1),addEdge(v,u,-1);
	}
	ll ans=0;
	for (int i=1;i<=n;++i) {
		if (vis[i]) continue;
		szn=szm=cnt[0]=cnt[1]=cnt[2]=flag=0,dfs(i,0);
		if (flag) ans+=1ll*szn*szn;
		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+=szm;
	}
	printf("%lld\n",ans);
	return 0;
}