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Problems > Bursting Balloons

Bursting Balloons

Difficulty: 2100 6000 ms 128 MB

dp interval-dp

Balloons in a row hold values a1..N. Bursting balloon i earns aleft·ai·aright, where left/right are the nearest UNBURST neighbours (value 1 beyond the ends). Maximize the total coins over all bursting orders.

Input: the first line has N; the second line has the N values.

Output: the maximum coins.

Constraints:

  • 1 ≤ N ≤ 500
  • 0 ≤ ai ≤ 100

Sample Tests

Input 1
4
3 1 5 8
Output 1
167
Input 2
1
5
Output 2
5

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