Counting on a directed graph | CodeChef

Counting on a directed graph

Problem code: GRAPHCNT

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Read problems statements in Mandarin Chinese and Russian.

Given an directed graph with N nodes (numbered from 1 to N) and M edges, calculate the number of unordered pairs (X, Y) such there exist two paths, one from node 1 to node X, and another one from node 1 to node Y, such that they don't share any node except node 1.

Input

There is only one test case in one test file.

The first line of each test case contains two space separated integers N, M. Each of the next M lines contains two space separated integers u, v denoting a directed edge of graph G, from node u to node v. There are no multi-edges and self loops in the graph.

Output

Print a single integer corresponding to the number of unordered pairs as asked in the problem..

Constraints and Subtasks

  • 1 ≤ N ≤ 105
  • 0 ≤ M ≤ 5 * 105

Subtask 1: (30 points)

Subtask 2: (20 points)

  • N * M ≤ 50000000


Subtask 3 (50 points)

  • No additional constraints

Example

Input:
6 6
1 2
1 3
1 4
2 5
2 6
3 6

Output:
14

Explanation

There are 14 pairs of vertices as follows:
(1,2)
(1,3)
(1,4)
(1,5)
(1,6)
(2,3)
(2,4)
(2,6)
(3,4)
(3,5)
(3,6)
(4,5)
(4,6)
(5,6)

Author: 5★ztxz16
Tester: 7★kevinsogo
Editorial http://discuss.codechef.com/problems/GRAPHCNT
Tags dominator, may15, medium-hard, ztxz16
Date Added: 25-03-2015
Time Limit: 2 sec
Source Limit: 50000 Bytes
Languages: C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS


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