## Critical Trade Bridge

There are `n`

islands from `0`

to `n-1`

. And the trades between these islands is mainly through the bridges connecting them.

**All the islands are connected**, i.e., there will always be a path between any two islands. There can be multiple paths as well.

Let's say there are islands A and B. And there is a direct bridge between A and B. If we remove this bridge, and if the trade between A and B is cut. Then such a bridge is called **critical bridges**.

Your task is to find all such bridges.

Example:

In the above graph, Bridge 1 and 2 is a critical because if it is disconnected then trade between 1 and 2 is cut.

Bridge between 2 and 3 is not critical because if it is disconnected then trade still continues through (2 -> 4 -> 3).

#### Input

The first line contains `n`

and `e`

where `n`

represents number of islands, `e`

represents number of bridges.

Next `e`

lines contains two integers `u`

, `v`

. This represents there is a bridge between `u`

and `v`

.

#### Output

The first line should contain `c`

-- number of critical bridges

The next `c`

lines contains two integers `u`

, `v`

. This represents bridge between `u`

and `v`

is a critical bridge.** u \(\lt\) v **

**Note**

- You must print answer in sorted order

Example: If critical bridges are: [(5, 7), (2, 1), (1, 0)]

Then you should print then as: [(0, 1), (1, 2), (5, 7)]

#### Constraints

1 \(\leq\) `n`

\(\leq 10^5\)

`n-1`

\(\leq\) `e`

\(\leq 10^5\)

#### Example

**Input**

```
4 4
0 1
1 2
2 3
1 3
```

**Output**

```
1
0 1
```

## Comments

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