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;

struct node{
	int t, nxt, flag;
}edge[200050];

int head[100050], cnt, typ[100050];

void add(int u, int v, int flag){
	edge[++cnt] = (node){v, head[u], flag};
	head[u] = cnt;
}

ll getans(int x){
	queue<int> q;
	typ[x] = 0;
	int cnt[3], edget = 0, dcnt = 1, flag1 = 0;
	cnt[0] = 1;
	cnt[1] = cnt[2] = 0;
	q.push(x);
	while(!q.empty()){
		int u = q.front(); q.pop();
		for(int i = head[u]; i; i = edge[i].nxt){
			int v = edge[i].t, ncol;
			if(edge[i].flag) edget++;
			if(typ[v]==-1) dcnt++;
			if(edge[i].flag == 1) ncol = (typ[u]+1) % 3;
			else ncol = (typ[u]+2)%3;
			if(typ[v]==-1){
				typ[v] = ncol;
				cnt[ncol]++;
				q.push(v);
			}
			else if(typ[v] != ncol) flag1 = 1; 
		}
	}
	if(flag1) return 1ll*dcnt * dcnt;
	else if(!cnt[0] || !cnt[1] || !cnt[2]) return edget;
	else {
		return 1ll*cnt[0] * cnt[1] + 1ll*cnt[1] * cnt[2] + 1ll*cnt[2] * cnt[0];
	}
}

int main(){
	ll ans = 0;
	int n, m;
	memset(typ, -1, sizeof(typ));
	scanf("%d %d", &n, &m);
	for(int i = 1; i <= m; i++){
		int u, v;
		scanf("%d %d", &u, &v);
		add(u, v, 1);
		add(v, u, 0);
	}
	for(int i = 1; i <= n; i++) if(typ[i] == -1){
		ans += getans(i);
	}
	printf("%lld", ans);
}