**Time limit:**1.00 s**Memory limit:**512 MB

Your task is to calculate the number of

*essential*connections: if such a connection is removed from the network, it is not possible to send a message between some two computers.

**Input**

The first input line contains an integer $n$: the number of computers. The computers are numbered $1,2,\ldots,n$.

After this, there are $n$ lines that describe the connections. Each line has two integers $a$ and $b$: there is a connection between computers $a$ and $b$.

There is at most one connection between two computers, and there are no connections from a computer to itself.

**Output**

Print one integer: the number of essential connections.

**Example**

Input:

`7`

1 2

2 3

2 4

4 5

2 5

5 6

6 7

Output:

`4`

Explanation: The essential connections are $(1,2)$, $(2,3)$, $(5,6)$ and $(6,7)$.

**Subtask 1 (28 points)**

- $2 \le n \le 100$

**Subtask 2 (72 points)**

- $2 \le n \le 10^5$