Problem D
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.

3 3
1 2
2 3
1 3

YES
1 3
2 1
3 2

4 3
1 2
1 3
1 4

NO

4 5
1 2
2 3
4 3
1 4
2 4

YES
1 4
2 1
2 4
3 2
4 3