Merging Tribes

In ancient times, there were $n$ tribes in the Kingdom of Jili. Each tribe was represented by an axis-aligned rectangle. Note that some regions might belong to multiple tribes.

Over time, if two tribes have a common overlapping area (i.e. intersection area strictly greater than zero), they merge into a new tribe. The new tribe is represented by the smallest axis-aligned rectangle that contains both original tribes. This process continues until no two tribes can merge.

Input Format: The first line contains an integer $n$. Each of the next $n$ lines contains four integers $x_1$, $y_1$, $x_2$, $y_2$, representing the bottom-left and top-right coordinates of a tribe's rectangle (with $x_1 < x_2$ and $y_1 < y_2$).

Output Format: First, output a single integer denoting the number of tribes remaining after all mergers. Then, output the coordinates of each tribe's rectangle on a separate line as four integers: $x_{\min}$, $y_{\min}$, $x_{\max}$, $y_{\max}$. The order of the tribes does not matter.

inputFormat

The first line contains an integer $n$ ($1\le n\le 10^5$). Each of the following $n$ lines contains four integers $x_1$, $y_1$, $x_2$, $y_2$ ($-10^9 \le x_1,y_1,x_2,y_2 \le 10^9$ with $x_1 < x_2$ and $y_1 < y_2$), representing a tribe's rectangle.

outputFormat

First, output an integer representing the number of remaining tribes. Then, for each tribe, output a line with four integers: $x_{\min}$, $y_{\min}$, $x_{\max}$, $y_{\max}$, which are the coordinates of the merged rectangle that covers all rectangles in that tribe.

sample

4
1 1 3 3
2 2 4 4
5 5 6 6
3 1 4 2

2
1 1 4 4
5 5 6 6