LogiQuest

83. Minimum Platforms

MediumSortingSweep Line

Given arrival and departure times (as HHMM integers) of n trains, print the minimum number of platforms so no train waits. A train departing at the same time another arrives needs a separate platform.

Input format

Line 1: n Line 2: n arrival times Line 3: n departure times

Output format

The minimum number of platforms.

Example 1

Input

6
900 940 950 1100 1500 1800
910 1200 1120 1130 1900 2000

Output

3

Example 2

Input

2
900 1000
1000 1100

Output

2

Constraints

1 ≤ n ≤ 10⁵ arrival ≤ departure

Read input from standard input and print the answer to standard output. Your code is judged against 5 test cases, most of them hidden.

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