# Problem J

Throwing bridges

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In the province of Wulingyuan in China, there are $N$ very steep cliffs. It is very popular for tourists to visit the mountain peaks.

Often, they even want to visit more than one in order to take photos from different angles. To facilitate this, several suspension bridges have been built so that one can walk from each mountain peak to all other mountain peaks. All was well until the High-altitude hijacker stole several bridges in the perfect heist - no one can catch up with you on the mountain peaks without using the bridges (which he just stole!). You have now been tasked with solving the problem with the bodybuilder John Xina to help you. He is so strong that he can rip out one of the remaining $M$ bridges and then throw it so that it connects two other mountains. However, this damages the bridges a little, so you want to avoid unnecessary throws. Help John Xina determine whether it is possible to perform throws so that one can walk between all pairs of mountain peaks. If it is possible, he wants to know which bridges to throw where. He also wants to make as few throws as possible. Even if John Xina cannot reach a certain bridge through other bridges, this is not a problem as he can climb down the mountain he is on and climb up any other mountain he wants.

## Input

The first row of input contains two integers, $N,M$ ($1 \leq N,M \leq 10^5$), the number of mountain peaks and the number of remaining bridges. Afterwards, $M$ lines follow, each containing two integers $u_ i$ and $v_ i$ ($1 \leq u_ i, v_ i \leq N$, $u_ i \neq v_ i$), which means that there is a bridge between $u_ i$ and $v_ i$. There is never more than one bridge between two mountain peaks.

## Output

Output “Ja” or “Nej”, whether or not it is possible to throw bridges so that one can walk between each pair of cliffs. If the answer is yes, output an integer $K$: the smallest number of throws needed. On the following $K$ rows, output four integers $u_1, v_1, u_2, v_2$, which describe that the bridge between $u_1$ and $v_1$ should be thrown so that it connects $u_2$ and $v_2$.

## Points

Your solution will be tested on a number of testgroups. To earn points in a testgroup all tests in it must succeed. For each subtask, if you correctly answer whether it is possible or not and correctly determine the minimum number of throws, but perform incorrect throws, you will receive $50\% $ of the subtask’s points.

Group |
Points |
Limits |

$1$ |
$20$ |
There are no cycles between mountains. |

$2$ |
$40$ |
$N, M \leq 1000$ |

$3$ |
$40$ |
No further restrictions |

Sample Input 1 | Sample Output 1 |
---|---|

5 4 1 2 2 3 1 3 4 5 |
Ja 1 1 3 1 4 |

Sample Input 2 | Sample Output 2 |
---|---|

9 9 1 2 2 3 1 3 4 5 5 6 4 6 7 8 8 9 7 9 |
Ja 2 1 3 1 4 4 6 4 7 |

Sample Input 3 | Sample Output 3 |
---|---|

2 0 |
Nej |