Maximum Gold Coins Collection

You are given a sequence of n boxes arranged in a row. Each box contains a certain number of gold coins. However, due to security restrictions, if you pick a box, you cannot pick its immediate neighbors. Your task is to determine the maximum total number of coins you can collect under this constraint.

You can formulate the problem using a dynamic programming approach. Let \(dp[i]\) represent the maximum number of coins that can be collected from the first \(i+1\) boxes. The recurrence relation can be written as:

[ dp[i] = \max(dp[i-1], dp[i-2] + coins[i]) ]

with the base cases:

[ dp[0] = coins[0], \quad dp[1] = \max(coins[0], coins[1]). ]

Your program should read the input from stdin and output the result to stdout.

inputFormat

The input consists of two lines:

• The first line contains an integer \(n\) — the number of boxes.
• The second line contains \(n\) space-separated integers, where each integer represents the number of coins in each box.

outputFormat

Output a single integer — the maximum number of coins that can be collected by picking boxes such that no two consecutive boxes are picked.

## sample

1
10

10