\begin{problem}{Highways}{highways.in}{highways.out}{2 seconds}

In a distant country Lineland there are $N$ cities and they are all
located along the highway. The highway is a straight line; it
starts from the first city and runs through the second, third city
and so on, ending in the $N$-th city. The $i$-th city is located at
the distance of $X_i$ miles from the first one.

The highway is wide and smooth, so it is a pleasure for all people
to drive along it. But there is one problem --- all roads in Lineland, including
the highway, are one-way.
So people are only allowed to drive along the highway from the city with
smaller number to the city with greater number and they have to use
country roads to get back, and that is not such a great pleasure indeed.

After the new president Mr.~Pathwayson was elected in Lineland, he has
decided that he would like to make it easier for people to get from one 
town to another. But he does not dare to change the traditions, and make 
the highway two-way. Therefore he has decided to build new highways 
to connect the cities, so that it would be possible to get from any city 
to any other one by highways.
Traditionally, the new highways must be one-way.

Of course, Mr.~Pathwayson is a great president, and he wants people to 
remember him in years. After a thought he has decided that building just 
one highway would not be enough for that. Therefore he has decided that 
he must build two new highways. Each highway would connect two different 
cities. Since people are anxious about their health, and cars running
along the highway produce dangerous wastes, each new highway must not 
pass through any cities, except the cities it connects. Also building two 
new highways in one city would disturb people too much, so all the cities 
that would be the ends of the new highways must be different.

You are the assistant of the minister of transportation of Lineland, so
you are asked to choose the cities to be connected by the new highways.
Since the cost of building a highway is proportional to its length, the
total length of the highways must be minimal possible. Write a program
to solve this problem. You may assume that the distance between two cities
along the new highway is equal to the distance between those cities along
the main highway.

\InputFile

The first line of the input file contains $N$ (${2 \le N \le 50\,000}$). 

Next line contains $N-1$ integer numbers: ${X_2, X_3, \ldots, X_N}$ 
(${1 \le X_2 < X_3 < \ldots < X_N  \le 10^9}$).

\OutputFile

If it is impossible to build the highways satisfying all requirements, print
number $0$ on the first line of the output file. 

In the other case on the first line of the output file print the minimal 
possible total length of the highways to be built. 
On the second line print $S_1$, $E_1$, $S_2$ and $E_2$ --- the numbers of the 
cities to connect by the first and the second highway, respectively. Note 
that highways are one-way and must run from $S_1$ to $E_1$ and from $S_2$ to $E_2$.

\Example

\begin{example}[*]
\exmp{
4
3 5 10
}{
12
3 1  4 2
}%
\end{example}

\end{problem}
