[2, 9]
  [3, 13]
  [3, 10]
  [3, 8]
  [3, 6]
  [3, 7]
  [4, 8]
  [4, 4]  *
  [4, 10]
  [5, 11]
  [7, 7]  *
  [7, 8]
  [7, 12]
  [7, 15]
  [9, 12]
  [9, 10] *

/*

Disjoint Intervals (https://www.interviewbit.com/problems/disjoint-intervals/)

    Asked in:
    Google

Problem Description

Given a set of N intervals denoted by 2D array A of size N x 2, the task is to find the length of maximal set of mutually disjoint intervals.

Two intervals [x, y] & [p, q] are said to be disjoint if they do not have any point in common.

Return a integer denoting the length of maximal set of mutually disjoint intervals.



Problem Constraints

1 <= N <= 105

1 <= A[i][0] <= A[i][1] <= 109



Input Format

First and only argument is a 2D array A of size N x 2 denoting the N intervals.


Output Format

Return a integer denoting the length of maximal set of mutually disjoint intervals.


Example Input

Input 1:

 A = [
       [1, 4]
       [2, 3]
       [4, 6]
       [8, 9]
     ]

Input 2:

 A = [
       [1, 9]
       [2, 3]
       [5, 7]
     ]



Example Output

Output 1:

 3

Output 2:

 2



Example Explanation

Explanation 1:

 Intervals: [ [1, 4], [2, 3], [4, 6], [8, 9] ]
 Intervals [2, 3] and [1, 4] overlap.
 We must include [2, 3] because if [1, 4] is included thenwe cannot include [4, 6].
 We can include at max three disjoint intervals: [[2, 3], [4, 6], [8, 9]]

Explanation 2:

 Intervals: [ [1, 9], [2, 3], [5, 7] ]
 We can include at max two disjoint intervals: [[2, 3], [5, 7]]
*/
int Solution::solve(vector<vector<int> > &A) {

    std::sort(A.begin(),A.end(),
        [](const vector<int>& op1, const vector<int>& op2){
            return (op1[0] < op2[0] );
        });

    int c = 1;
    auto it = A.begin();
    for (auto jt = A.begin()+1; jt != A.end(); ++jt){
        if (it->at(1) < jt->at(0)){
            c++;
            it = jt;
        } if (jt->at(1) < it->at(1)){
            it = jt;
        }
    }
    return c;
}