Mock CCO '18 Contest 4 Problem 1 - Mining for Minerals

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Points: 15 (partial)
Time limit: 0.5s
Memory limit: 64M

Problem type

The Zerg army is working on mining more minerals. They have found a mineral patch of length L. They have a single drone who will mine the minerals.

This drone needs to divide this mineral patch into sections of length L_1 through L_N. The drone can cut a mineral patch of length x into two mineral patches, one with length y and the other with length x-y. It will take the drone x seconds to perform one such cut. It is guaranteed that \sum_{i=1}^N L_i = L. The patches are unordered.

What is the minimum amount of time it will take this single drone to divide the mineral patch into the desired sections?


1 \le N \le 20 \cdot 10^3

1 \le L_i \le 50 \cdot 10^3

Input Specification

The first line will contain a single integer N.

Each of the next N lines will contain a single integer, L_i.

Output Specification

Output the number of seconds it will take for the drone to divide the mineral patch accordingly.

Sample Input


Sample Output