# One-Way Roads

In the ACM kingdom, there are $N$ cities connected by $M$ two-way roads. These cities are connected, i.e., one can reach from any city $X$ to any other city $Y$ by going through some of these roads. One day, the government wishes to assign for each road a direction, such that one can still reach from any city to any other. You are asked to determine whether this task is possible.

## Input

The first line of each test case consists of two integers, $N$ ($1 \leq N \leq 50$), and $M$ ($1 \leq M \leq N(N - 1)/2$). Each of the next $M$ lines describes a road, and consists of two integers, $X$ and $Y$, ($1 \leq X, Y \leq N$; $X \neq Y$), indicating that there is a road between city $X$ and $Y$. There is at most one road that directly connects each pair of cities.

## Output

If it is impossible, output a single line `NO`. Otherwise, output `YES` on the first line, followed by $M$ lines describing one possible
direction assignment to these $M$ roads. Each of these $M$ lines should consist of two
integers, $X$,
$Y$, indicating that there
is a one-way road from city $X$ to city $Y$. These $M$ lines can be output in any
order.

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

3 3 1 2 2 3 1 3 |
YES 1 3 2 1 3 2 |

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

4 3 1 2 1 3 1 4 |
NO |

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

4 5 1 2 2 3 4 3 1 4 2 4 |
YES 1 4 2 1 2 4 3 2 4 3 |