Matcom Online Grader
Faculty of Mathematics and Computer Science of University of Havana

The sequence $a_1, a_2, \ldots, a_n$ is called a permutation, if it contains every integer from 1 to $n$.

The permutation of vertices $a_1, a_2, \ldots, a_n$ is a topological sort of a directed graph, if for every directed edge from $u$ to $v$, vertex $u$ comes before $v$ in this permutation.

The permutation $a_1, a_2, \ldots, a_n$ is lexicographically smaller than the permutation $b_1, b_2, \ldots, b_n$, if there exists $m$ such that $a_i = b_i$ for every $1 \le i < m$ and $a_m < b_m$.

Given a directed acyclic graph, add at most $k$ directed edges to it in such a way, that the resulting graph still has no cycles and the lexicographically minimal topological sort of the graph is maximum possible.

The first line of the input file contains three integers $n$, $m$ and $k$ — the number of vertices and directed edges in the original graph, and the number of  directed edges, that you are allowed to add ($1 \le n \le 100\,000$; $0 \le m, k \le 100\,000$).

The first line of the output file should contain $n$ integers — the lexicographically minimal topological sort of the modified graph. The second line should contain a single integer $x$ ($0 \le x \le k$) — the number of directed edges to add. The following $x$ lines of the output should contain description of added directed edges in the same format as in the input file.