Bridges

King Julian rules over $n$ islands, numbered from 1 to $n$. Some pairs of islands are connected by bridges that can be crossed in both directions. There are $m$ bridges in total. Any island can be reached from any other island by moving across the bridges.

A bridge is critical if, when it collapses, there exist two islands such that one cannot be reached from the other using the remaining bridges.

King Julian is worried about the safety and reliability of communication in his realm. He wants to build additional bridges between some pairs of islands so that no critical bridge remains. Since he is also thrifty, he wants to find the minimum number of additional bridges needed to meet this requirement.

The first line contains two integers $n$ and $m$, the number of islands and the number of bridges ($2 \le n \le 100000$, $1 \le m \le 200000$). Each of the next $m$ lines contains two integers $a_i$ and $b_i$, the islands connected by the $i$-th bridge ($1 \le a_i, b_i \le n$, $a_i \neq b_i$).

It is guaranteed that any island can be reached from any other island by moving across the bridges.

Print one integer: the minimum number of additional bridges that must be built so that no critical bridges remain.