Alignment |
Solution |
Tests |

In the army, a platoon is composed by n soldiers. During the morning inspection, the soldiers are aligned in a straight line in front of the captain. The captain is not satisfied with the way his soldiers are aligned; it is true that the soldiers are aligned in order by their code number: 1 , 2 , 3 , . . . , n , but they are not aligned by their height. The captain asks some soldiers to get out of the line, as the soldiers that remain in the line, without changing their places, but getting closer, to form a new line, where each soldier can see by looking lengthwise the line at least one of the line’s extremity (left or right). A soldier see an extremity if there isn’t any soldiers with a highest or equal height than his height between him and that extremity.

Task

Write a program that, knowing the height of each soldier, determines the minimum number of soldiers which have to get out of line, as the new line to accomplish the condition from the utterance.

Input format

On the first line of the input file **ALINIERE.IN **is written the number of the soldiers **n**. On the second line is written a series of **n** floating numbers with at most 5 digits precision and separated by a space character. The k-th number from this line represents the height of the soldier who has the code k (1£
k£
n).

Output format

The output file **ALINIERE.OUT** will contain on the first line the number of the soldiers who have to get out of the line and on the next line their codes in ascending order, separated by a space character. Even if there is more than one solution, the program will display only one solution .

Restrictions

- 2 £ n £ 1000
- the height are floating numbers from the interval [0.5; 2.5]

Example

ALINIERE.IN

8

1.86 1.86 1.30621 2 1.4 1 1.97 2.2

ALINIERE.OUT

4

1 3 7 8

Explanation

The new line is composed by the soldiers who have the codes: 2, 4, 5, 6 and having

the heights: 1.86 2 1.4 1.

The soldier who has the code 2 sees the left extremity .

The soldier who has the code 4 sees the both extremities .

The soldiers who have the codes 5 and 6 see the right extremity .

Time limit: 1 second/test