Algorithms and Data Structures

Staircase with a cost

You’re climbing a staircase with n stairs. On each step, you can either climb 2 stairs or climb only 1. As you step on each stair, you pay a cost associated with that stair. Your task is to climb to the very top by paying as little as possible.

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 1000).
The next line contains the costs associated with each stair (0 ≤ ≤ 1000).

Output

The program should print the minimum cost to reach the top of the staircase.

Examples

Input
Output
3 10 12 25
12
10 1 20 1 1 1 20 1 2 20 1
7

Explanation

  1. We stand in front of the staircase ⇒ the current cost is 0. We step on the second staircase ⇒ the cost is 12. Then we get out of the staircase by doing a step of length 2 ⇒ cost remains 12.
  1. 1 20 1 1 1 20 1 2 20 1 ⇒ 1 20 1 1 1 20 1 2 20 1 ⇒ 1 20 1 1 1 20 1 2 20 1 ⇒ 1 20 1 1 1 20 1 2 20 1 ⇒ 1 20 1 1 1 20 1 2 20 1 ⇒ 1 20 1 1 1 20 1 2 20 1 ⇒ 1 20 1 1 1 20 1 2 20 1 ⇒ 7
 

Constraints

Time limit: 2 seconds

Memory limit: 512 MB

Output limit: 1 MB

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