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;

using ll = long long;

const int MAXN = 100010;
int N, M;
vector<pair<int, int>> adj[MAXN];

int t[MAXN];
int nEdges;
ll freq[3];

bool dfs(int v, int c) {
	bool valid = true;
	t[v] = c;
	freq[c]++;
	for (auto e : adj[v]) {
		nEdges++;
		int newc = (c + e.second) % 3;
		if (t[e.first] == -1) {
			valid &= dfs(e.first, newc);
		} else {
			valid &= (newc == t[e.first]);
		}
	}
	return valid;
}

int main() {
	scanf("%d %d", &N, &M);
	for (int i = 0; i < M; i++) {
		int a, b; scanf("%d %d", &a, &b); a--, b--;
		adj[a].emplace_back(b, 1);
		adj[b].emplace_back(a, 2);
	}

	ll ans = 0;
	fill_n(t, N, -1);
	for (int i = 0; i < N; i++) {
		if (t[i] != -1) continue;
		nEdges = 0;
		freq[0] = freq[1] = freq[2] = 0;
		if (dfs(i, 0)) {
			if (!freq[0] || !freq[1] || !freq[2]) {
				ans += nEdges / 2;
			} else {
				ans += freq[0]*freq[1] + freq[1]*freq[2] + freq[2]*freq[0];
			}
		} else {
			ll tot = freq[0] + freq[1] + freq[2];
			ans += tot*tot;
		}
	}
	printf("%lld\n", ans);
	
	return 0;
}