The Byteburg's street network consists of ~n~ intersections linked by ~m~ two-way street segments. Recently, the Byteburg was chosen to host the upcoming duathlon championship. This competition consists of two legs: a running leg, followed by a cycling leg.

The route for the competition should be constructed in the following way. First, three distinct intersections ~s~, ~c~, and ~f~ should be chosen for start, change, and finish stations. Then the route for the competition should be built. The route should start in ~s~, go through ~c~ and end in ~f~. For safety reasons, the route should visit each intersection at most once.

Before planning the route, the mayor wants to calculate the number of ways to choose intersections ~s~, ~c~, and ~f~ in such a way that it is possible to build the route for them. Help him to calculate this number.

Input

The first line contains integers ~n~ and ~m~: number of intersections, and number of roads. Next ~m~ lines contain descriptions of roads ~(1 \le n \le 10^5, 1 \le m \le 2 \cdot 10^5)~. Each road is described with pair of integers ~v_i~, ~u_i~, the indices of intersections connected by the road ~(1 \le v_i, u_i \le n, v_i \ne u_i)~. For each pair of intersections, there is at most one road connecting them.

Output

Output the number of ways to choose intersections ~s~, ~c~, and ~f~ for start, change, and finish stations, in such a way that it is possible to build the route for competition.

Scoring

Subtask 1 (points: 5)

~n \le 10~, ~m \le 100~

Subtask 2 (points: 11)

~n \le 50~, ~m \le 100~

Subtask 3 (points: 8)

~n \le 100\,000~, there are at most two roads that end in each intersection.

Subtask 4 (points: 10)

~n \le 1\,000~, there are no cycles in the street network. The cycle is the sequence of ~k~ ~(k \ge 3)~ distinct intersections ~v_1, v_2, \dots, v_k~, such that there is a road connecting ~v_i~ with ~v_{i+1}~ for all ~i~ from ~1~ to ~k-1~, and there is a road connecting ~v_k~ and ~v_1~.

Subtask 5 (points: 13)

~n \le 100\,000~, there are no cycles in the street network.

Subtask 6 (points: 15)

~n \le 1\,000~, for each intersection there is at most one cycle that contains it.

Subtask 7 (points: 20)

~n \le 100\,000~, for each intersection there is at most one cycle that contains it.

Subtask 8 (points: 8)

~n \le 1\,000~, ~m \le 2\,000~

Subtask 9 (points: 10)

~n \le 100\,000~, ~m \le 200\,000~

Sample Input 1

4 3
1 2
2 3
3 4

Sample Output 1

8

Sample Input 2

4 4
1 2
2 3
3 4
4 2

Sample Output 2

14

Explanation

In the first example there are 8 ways to choose the triple ~(s, c, f)~: ~(1, 2, 3)~, ~(1, 2, 4)~, ~(1, 3, 4)~, ~(2, 3, 4)~, ~(3, 2, 1)~, ~(4, 2, 1)~, ~(4, 3, 1)~, ~(4, 3, 2)~.

In the second example there are 14 ways to choose the triple ~(s, c, f)~: ~(1, 2, 3)~, ~(1, 2, 4)~, ~(1, 3, 4)~, ~(1, 4, 3)~, ~(2, 3, 4)~, ~(2, 4, 3)~, ~(3, 2, 1)~, ~(3, 2, 4)~, ~(3, 4, 1)~, ~(3, 4, 2)~, ~(4, 2, 1)~, ~(4, 2, 3)~, ~(4, 3, 1)~, ~(4, 3, 2)~.