Algorithms and Data Structures

Wine production

You are responsible for the logistics of a wine production factory. There are n containers and every day one container is filled with wine. For each container, you know the number of days it should be kept closed before opening. You’d like to minimize the time it will take to open all the containers.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ ).
The next line contains n space-separated integers (1 ≤ ≤ ) the number of days each of the containers need to be kept closed before opening.

Output

The program should print the least amount of time you need to wait until all the containers can be opened.

Examples

Input
Output
4 2 3 4 3
6
6 39 19 38 39 22 35
41

Explanation

  • Example 1 (enumerated numbers represent the day numbers):
      1. Fill the container that needs to be kept closed for 4 days
      1. Fill the container that needs to be kept closed for 3 days
      1. Fill the container that needs to be kept closed for 3 days
      1. Fill the container that needs to be kept closed for 2 days
      1. Open the containers filled during Day 1 and Day 2
      1. Open the containers filled during Day 3 and Day 4 ⇒ all are open
 

Constraints

Time limit: 2.4 seconds

Memory limit: 512 MB

Output limit: 1 MB

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