You need to implement the algorithm for both the interval scheduling and the interval partitioning problem. Please provide the solution for the interval scheduling problem in the first line of the output, and the solution for the interval partitioning problem in the second line of the output. An O$($nlogn$)-$time algorithm is sufficient to pass any feasible test cases.

$($a$)$ Input You need to read the input from the console. In the first line of the input, we have one positive integer n$.$ n is the number of intervals. The intervals are indexed from $1$ to n$.$ You can assume that $1<=$ n $<=100000.$ In the next n lines, each line contains $2$ integers: si and fi$.$ This indicates that there is an interval $($si$,$fi$).$

$($b$)$ Output You need to output to the console. The output consists of two lines: the number of jobs in the first line and the number of machines in the second line.

Below are examples of input and output:

Example input: Example output:

$105$

$124$

$56$

$13$

$34$

$410$

$56$

$45$

$79$

$57$

$24$