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>
#include<cstring>
#include<iostream>
#include<algorithm>
#define ll long long

using namespace std;

inline void Rd(int &res) {
	char c; res = 0;
	while (c = getchar(), c < '0');
	do {
		res = (res << 1) + (res << 3) + (c ^ 48);
	} while (c = getchar(), c >= '0');
}

const int M = (int) 1e5 + 5;

ll ans;
bool flag;
int n, m, Head[M], tot, col[M], sz[3], cntedge;
struct Node {int to, nxt, type;} Edge[M << 1];

inline void Addedge(int a, int b) {
	Edge[tot] = (Node) {b, Head[a], 1}; Head[a] = tot++;
	Edge[tot] = (Node) {a, Head[b], -1}; Head[b] = tot++;
}

void dfs(int x) {
	sz[col[x]]++;
	for (int i = Head[x]; ~i; i = Edge[i].nxt) {
		int to = Edge[i].to;
		cntedge += (Edge[i].type == 1);
		if (col[to] == -1) col[to] = (col[x] + Edge[i].type + 3) % 3, dfs(to);
		else if (col[to] != (col[x] + Edge[i].type + 3) % 3) flag = false;
	}
}

int main() {
	Rd(n), Rd(m);
	memset(col, -1, sizeof(col));
	memset(Head, -1, sizeof(Head));
	while (m--) {
		int a, b;
		Rd(a), Rd(b);
		Addedge(a, b);
	}
	for (int i = 1; i <= n; i++) {
		if (~col[i]) continue;
		col[i] = 0, flag = true, cntedge = 0;
		memset(sz, 0, sizeof(sz));
		dfs(i);
		if (!flag) ans += (ll) (sz[0] + sz[1] + sz[2]) * (sz[0] + sz[1] + sz[2]);
		else if (!sz[1] || !sz[2]) ans += cntedge;
		else ans += (ll) sz[0] * sz[1] + (ll) sz[1] * sz[2] + (ll) sz[2] * sz[0];
	}
	cout << ans << endl;
	return 0;
}