Minimum Arrow Shots

The first line of input contains an integer 'N', the number of balloons.

The next 'N' lines each contain two space-separated integers, x_start and x_end.

Print a single integer representing the minimum number of arrows required.

A key insight to solve this problem greedily is to sort the balloons. Sorting by the end coordinate (x_end) is a highly effective strategy.

Sample Input 1:

4
10 16
2 8
1 6
7 12

Sample Output 1:

2

Explanation for Sample 1:

Sort the balloons by their end points: `[1,6], [2,8], [7,12], [10,16]`.
1.  Shoot the first arrow at x=6 to burst the `[1,6]` balloon. This arrow's position is now 6.
2.  Consider the `[2,8]` balloon. Its start (2) is less than or equal to the arrow's position (6). So, this balloon is also burst by the same arrow.
3.  Consider the `[7,12]` balloon. Its start (7) is greater than the arrow's position (6). We need a new arrow. Increment arrow count to 2. Shoot this new arrow at x=12. The new arrow's position is 12.
4.  Consider the `[10,16]` balloon. Its start (10) is less than or equal to the new arrow's position (12). This balloon is also burst.
All balloons are burst with 2 arrows.

Sample Input 2:

4
1 2
3 4
5 6
7 8

Sample Output 2:

4

Explanation for Sample 2:

The balloons `[1,2], [3,4], [5,6], [7,8]` have no overlapping horizontal diameters. Therefore, each balloon requires its own arrow.

Expected Time Complexity:

The expected time complexity is O(N log N).

Constraints:

1 <= N <= 10^5
-2^31 <= x_start < x_end <= 2^31 - 1

Time limit: 1 sec