Problem Statement

You are at a conveyor belt sushi restaurant.
N plates of sushi come along the belt in order. The deliciousness of each of the N plates of sushi is represented by \(V_i\).

You can take a plate of sushi when it comes in front of you, but under this restaurant's rules,
you cannot take plates consecutively.
Of course, you also cannot take sushi that has already passed in front of you.

Find the maximum total deliciousness you can obtain and the numbers of the plates you took (numbered starting from 1) in ascending order.
The sushi does not come around a second time.

Input

\(N \)
\(V_1\,V_2\,V_3 \ldots V_N \)

The first line contains the number of sushi plates \(N (1\le N \le 1000)\).
The second line contains the deliciousness of the $i$-th sushi \( V_i (1\le V_i \le 100,1 \le i \le N) \), separated by single spaces.

Output

Output the maximum total deliciousness you can obtain on the first line, and
the numbers of the plates you took (1-indexed), separated by spaces, on the second line.
If there are multiple answers, output any one of them.
If there is no answer at all, you may eat whatever sushi you like.

Sample

4
1 2 3 4

6
2 4

4
5 4 4 9

14
1 4

7
1 2 9 10 1 1 4

16
2 4 7

1
100

100
1