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

A component is a group of cities where there is a route between any two cities using the roads. After each day, your task is to find the number of components and the size of the largest component.

**Input**

The first input line has two integers $n$ and $m$: the number of cities and roads. The cities are numbered $1,2,\dots,n$.

Then, there are $m$ lines describing the new roads. Each line has two integers $a$ and $b$: a new road is constructed between cities $a$ and $b$.

You may assume that every road will be constructed between two different cities.

**Output**

Print $m$ lines: the required information after each day.

**Constraints**

- $1 \le n \le 10^5$

- $1 \le m \le 2 \cdot 10^5$

- $1 \le a,b \le n$

**Example**

Input:

`5 3`

1 2

1 3

4 5

Output:

`4 2`

3 3

2 3