Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ACM-ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

C2. Brain Network (medium)

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputFurther research on zombie thought processes yielded interesting results. As we know from the previous problem, the nervous system of a zombie consists of *n* brains and *m* brain connectors joining some pairs of brains together. It was observed that the intellectual abilities of a zombie depend mainly on the topology of its nervous system. More precisely, we define the distance between two brains *u* and *v* (1 ≤ *u*, *v* ≤ *n*) as the minimum number of brain connectors used when transmitting a thought between these two brains. The brain latency of a zombie is defined to be the maximum distance between any two of its brains. Researchers conjecture that the brain latency is the crucial parameter which determines how smart a given zombie is. Help them test this conjecture by writing a program to compute brain latencies of nervous systems.

In this problem you may assume that any nervous system given in the input is valid, i.e., it satisfies conditions (1) and (2) from the easy version.

Input

The first line of the input contains two space-separated integers *n* and *m* (1 ≤ *n*, *m* ≤ 100000) denoting the number of brains (which are conveniently numbered from 1 to *n*) and the number of brain connectors in the nervous system, respectively. In the next *m* lines, descriptions of brain connectors follow. Every connector is given as a pair of brains *a* *b* it connects (1 ≤ *a*, *b* ≤ *n* and *a* ≠ *b*).

Output

Print one number – the brain latency.

Examples

Input

4 3

1 2

1 3

1 4

Output

2

Input

5 4

1 2

2 3

3 4

3 5

Output

3

Codeforces (c) Copyright 2010-2018 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Mar/23/2018 08:19:25 (d3).

Desktop version, switch to mobile version.

User lists

Name |
---|