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;
const int N = 1e5 + 100;

struct edge {
	int u, w;
	edge(int u, int w): u(u), w(w) {}
};

int f(int x, int y) {
	return (x + y + 3) % 3;
}

ll n, m, ans, edge_cnt, cnt[3], c[N];
vector<int> vec;
bool mark[N];
vector<edge> nei[N];

bool dfs(int v) {
	vec.push_back(v);
	bool b = true;
	mark[v] = true;
	cnt[c[v]]++;
	for (edge e: nei[v]) {
		edge_cnt++;
		if (mark[e.u] == false) {
			c[e.u] = f(c[v], e.w);
			b &= dfs(e.u);
		}
		else if (c[e.u] != f(c[v], e.w))
			b = false;
	}
	return b;
}

bool ok(vector<int> vec) {
	for (int v: vec)
		for (int i = 1; i < nei[v].size(); i++)
			if (nei[v][i - 1].w != nei[v][i].w)
				return true;
	return false;
}

ll solve(int v) {
	edge_cnt = 0;
	memset(cnt, 0, sizeof cnt);
	vec.clear();
	if (dfs(v) == false)
		return (cnt[0] + cnt[1] + cnt[2]) * (cnt[0] + cnt[1] + cnt[2]);
	if (ok(vec) == false)
		return edge_cnt / 2;
	return cnt[0] * cnt[1] + cnt[1] * cnt[2] + cnt[2] * cnt[0];
}

int main() {
	ios::sync_with_stdio(false), cin.tie(0);
	cin >> n >> m;
	while (m--) {
		int x, y;
		cin >> x >> y;
		nei[--x].push_back(edge(--y, 1));
		nei[y].push_back(edge(x, -1));
	}
	for (int v = 0; v < n; v++)
		if (mark[v] == false)
			ans += solve(v);
	cout << ans;
}