To meet the ever-growing demands of his N (1
To meet the ever-growing demands of his N (1 <= N <= 50,000) cows, Farmer John has bought them a new soda machine. He wants to figure out the perfect place to install the machine. The field in which the cows graze can be represented as a one-dimensional number line. Cow i grazes in the range A_i..B_i A i ..B i (1<= A_i A i <= B_i B i ; A_i A i <= B_i B i <= 1,000,000,000) (a range that includes its endpoints), and FJ can place the soda machine at any integer point in the range 1..1,000,000,000. Since cows are extremely lazy and try to move as little as possible, each cow would like to have the soda machine installed within her grazing range. Sadly, it is not always possible to satisfy every cow's desires. Thus FJ would like to know the largest number of cows that can be satisfied. To demonstrate the issue, consider four cows with grazing ranges 3..5, 4..8, 1..2, and 5..10; below is a schematic of their grazing ranges: 1 2 3 4 5 6 7 8 9 10 11 12 13 |---|---|---|---|---|---|---|---|---|---|---|---|-... aaaaaaaaa bbbbbbbbbbbbbbbbb ccccc ddddddddddddddddddddd As can be seen, the first, second and fourth cows share the point 5, but the third cow's grazing range is disjoint. Thus, a maximum of 3 cows can have the soda machine within their grazing range.
