Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

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

D. Metro Scheme

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputBerland is very concerned with privacy, so almost all plans and blueprints are secret. However, a spy of the neighboring state managed to steal the Bertown subway scheme.

The Bertown Subway has *n* stations, numbered from 1 to *n*, and *m* bidirectional tunnels connecting them. All Bertown Subway consists of lines. To be more precise, there are two types of lines: circular and radial.

A radial line is a sequence of stations *v*_{1}, ..., *v*_{k} (*k* > 1), where stations *v*_{i} and *v*_{i + 1} (*i* < *k*) are connected by a tunnel and no station occurs in the line more than once (*v*_{i} ≠ *v*_{j} for *i* ≠ *j*).

A loop line is a series of stations, *v*_{1}, ..., *v*_{k} (*k* > 2), where stations *v*_{i} и *v*_{i + 1} are connected by a tunnel. In addition, stations *v*_{1} and *v*_{k} are also connected by a tunnel. No station is occurs in the loop line more than once.

Note that a single station can be passed by any number of lines.

According to Berland standards, there can't be more than one tunnel between two stations and each tunnel belongs to exactly one line. Naturally, each line has at least one tunnel. Between any two stations there is the way along the subway tunnels. In addition, in terms of graph theory, a subway is a vertex cactus: if we consider the subway as a graph in which the stations are the vertexes and the edges are tunnels, then each vertex lies on no more than one simple cycle.

Unfortunately, scheme, stolen by the spy, had only the stations and the tunnels. It was impossible to determine to which line every tunnel corresponds. But to sabotage successfully, the spy needs to know what minimum and maximum number of lines may be in the Bertown subway.

Help him!

Input

The first line contains two integers *n* and *m* (1 ≤ *n* ≤ 10^{5}, 0 ≤ *m* ≤ 3·10^{5}) — the number of stations and the number of tunnels, correspondingly.

Each of the next *m* lines contain two integers — the numbers of stations connected by the corresponding tunnel. The stations are numbered with integers from 1 to *n*.

It is guaranteed that the graph that corresponds to the subway has no multiple edges or loops, it is connected and it is a vertex cactus.

Output

Print two numbers — the minimum and maximum number of lines correspondingly.

Examples

Input

3 3

1 2

2 3

3 1

Output

1 3

Input

8 8

1 2

2 3

3 4

4 5

6 4

4 7

7 2

2 8

Output

2 8

Input

6 6

1 2

2 3

2 5

5 6

3 4

3 5

Output

3 6

Note

The subway scheme with minimum possible number of lines for the second sample is:

Codeforces (c) Copyright 2010-2017 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Sep/22/2017 09:04:18 (c3).

Desktop version, switch to mobile version.

User lists

Name |
---|