Longest Increasing Sequence

Time passed and Taro became a high school student. Under the influence of my older brother who was a college student, I began to be interested in computer science. Taro read through computer science textbooks and learned that there was a famous problem called the "longest increase subsequence problem." Taro understood this problem, but was wondering if he could create a similar problem himself. Therefore, Taro created the following problem as a result of trial and error.

• There is a sequence A consisting of n integers
• Decompose the sequence A into m sequences with m-1 delimiters. In addition, each sequence after decomposition must always include one or more numbers.
• If the m numbers created by adding all the integers in each of these m sequences are arranged in the order of the original sequence, it becomes a strict increasing sequence (that is, the resulting sequence is Bi <Bi + 1). I want to do it.
• The goal is to maximize the length m of the final sequence B.

For example, consider the case where the sequence A is {5, -4,10, -3,8}. Prepare a sequence C that represents the position of the delimiter, and set C = {2,4}. At this time, the sequence A is divided into the parts (5, -4), (10, -3), (8), and when these interiors are added together, they become 1,7,8, respectively, and the resulting sequence B is {1, 7,8}.

Taro named this problem the "longest increase subsequence problem" and also considered an algorithm to solve it. And I contacted you as a member of society to check it. Your job is to create a program to solve the problems created by Taro who has grown up. Since it is my job to check, it also outputs the position of the m-1 delimiter. In addition, there may be multiple such delimiters for the optimum m, but if this m is output correctly, one of the possible ones should be output.

Constraints

1 ≤ n ≤ 4000 | Ai | ≤ 108

• For the integer k, | k | represents the absolute value of k

Input

N + 1 integers are given, separated by line breaks.

n A1 A2 ... An

• n represents the length of the given sequence A
• Ai represents the i-th element of the sequence A.

Output

m C1 C2 .. Cm-1

• The first line outputs one integer m. m represents the length of the final sequence B. The second line outputs m-1 integer Ci separated by blanks. Ci represents the i-th delimiter when the sequence A is appropriately divided into m parts. See the figure for the definition of the delimiter. Note that 1 ≤ Ci <n is satisfied. The m-1 integer sequence C in the second row must be arranged in ascending order. Therefore, if i <j, then Ci <Cj holds.

• If m = 1, the second line will be blank.

• When the sequence B is generated from the sequence A according to the sequence C, when the sequence B is not an increasing sequence (that is, when i (1 ≤ i <m) such that Bi ≥ Bi + 1 exists), it becomes WrongAnswer.

Examples

Input

3 1 2 4

Output

3 1 2

Input

3 2 2 2

Output

2 1

Input

3 4 2 1

Output

1 (空行)

inputFormat

outputFormat

outputs the position of the m-1 delimiter. In addition, there may be multiple such delimiters for the optimum m, but if this m is output correctly, one of the possible ones should be output.

Constraints

1 ≤ n ≤ 4000 | Ai | ≤ 108

• For the integer k, | k | represents the absolute value of k

Input

N + 1 integers are given, separated by line breaks.

n A1 A2 ... An

• n represents the length of the given sequence A
• Ai represents the i-th element of the sequence A.

Output

m C1 C2 .. Cm-1

• The first line outputs one integer m. m represents the length of the final sequence B. The second line outputs m-1 integer Ci separated by blanks. Ci represents the i-th delimiter when the sequence A is appropriately divided into m parts. See the figure for the definition of the delimiter. Note that 1 ≤ Ci <n is satisfied. The m-1 integer sequence C in the second row must be arranged in ascending order. Therefore, if i <j, then Ci <Cj holds.

• If m = 1, the second line will be blank.

• When the sequence B is generated from the sequence A according to the sequence C, when the sequence B is not an increasing sequence (that is, when i (1 ≤ i <m) such that Bi ≥ Bi + 1 exists), it becomes WrongAnswer.

Examples

Input

3 1 2 4

Output

3 1 2

Input

3 2 2 2

Output

2 1

Input

3 4 2 1

Output

1 (空行)

样例

3
4
2
1

1
(空行)

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