Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

H. Road Problem

time limit per test

3 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe Berland capital (as you very well know) contains *n* junctions, some pairs of which are connected by two-way roads. Unfortunately, the number of traffic jams in the capital has increased dramatically, that's why it was decided to build several new roads. Every road should connect two junctions.

The city administration noticed that in the cities of all the developed countries between any two roads one can drive along at least two paths so that the paths don't share any roads (but they may share the same junction). The administration decided to add the minimal number of roads so that this rules was fulfilled in the Berland capital as well. In the city road network should exist no more than one road between every pair of junctions before or after the reform.

Input

The first input line contains a pair of integers *n*, *m* (2 ≤ *n* ≤ 900, 1 ≤ *m* ≤ 100000), where *n* is the number of junctions and *m* is the number of roads. Each of the following *m* lines contains a description of a road that is given by the numbers of the connected junctions *a*_{i}, *b*_{i} (1 ≤ *a*_{i}, *b*_{i} ≤ *n*, *a*_{i} ≠ *b*_{i}). The junctions are numbered from 1 to *n*. It is possible to reach any junction of the city from any other one moving along roads.

Output

On the first line print *t* — the number of added roads. Then on *t* lines print the descriptions of the added roads in the format of the input data. You can use any order of printing the roads themselves as well as the junctions linked by every road. If there are several solutions to that problem, print any of them.

If the capital doesn't need the reform, print the single number 0.

If there's no solution, print the single number -1.

Examples

Input

4 3

1 2

2 3

3 4

Output

1

1 4

Input

4 4

1 2

2 3

2 4

3 4

Output

1

1 3

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Aug/17/2017 20:13:30 (c2).

Desktop version, switch to mobile version.

User lists

Name |
---|