Consider a connected undirected graph. A node is called an articulation point if its removal disconnects the graph. Similarly, an edge is called a bridge if its removal disconnects the graph.

Your task is to calculate the number of articulation points and bridges in the graph.

Input

The first line contains two integers n and m: the number of nodes and edges in the graph. The nodes are numbered 1,2,\ldots,n.

Then, there are m lines that describe the edges. Each line contains two values a and b: there is an edge between nodes a and b.

Output

Output two integers: the number of articulation points and bridges.

Constraints

• 1 \le n \le 10^5
• 1 \le m \le 2 \cdot 10^5

Example

Input:

7 8
1 2
1 3
2 3
3 4
4 5
4 6
5 6
5 7

Output:

3 2

Explanation: Nodes 3, 4, and 5 are articulation points, and edges (3,4) and (5,7) are bridges.