Hierarchical Calculator

Time Limit : 2 sec, Memory Limit : 262144 KB
Japanese version is here

B: Hierarchical Calculator

Problem

Ebi-chan has N formulae: y = a_i x for i =1, ..., N (inclusive). Now she considers a subsequence of indices with length k: s_1, s_2, ..., s_k. At first, let x_0 be 1 and evaluate s_1-th formulae with x = x_0. Next, let x_1 be the output of s_1 and evaluate s_2-th formulae with x = x_1, and so on.

She wants to maximize the final output of the procedure, x_{s_k}. If there are many candidates, she wants the """shortest one""". If there are still many candidates, she wants the """lexicographically smallest one""".

Sequence s is lexicographically smaller than sequence t, if and only if either of the following conditions hold:

  • there exists m < |s| such that s_i = t_i for i in 1 to m (inclusive) and s_{m+1} < t_{m+1}, or
  • s_i = t_i for i in 1 to |s| (inclusive) and |s| < |t|,

where |s| is the length of the s.

Input

N
a_1 a_2 $\cdots$ a_N

Constraints

  • 1 \leq N \leq 60
  • -2 \leq a_i \leq 2 for i=1, ...,N (inclusive)
  • Every input is given as the integer.

Output

Output k+1 lines. First line, the length of the sequence, k. Following k lines, the index of the i-th element of the subsequence, s_i (one element per line).

Sample Input 1

4
2 0 -2 1

Sample Output for Input 1

1
1

She evaluates the first one and gets the maximum value 2.

Sample Input 2

3
2 -2 -2

Sample Output for Input 2

3
1
2
3

She evaluates all of them and gets the maximum value 8.

Sample Input 3

2
-1 0

Sample Output for Input 3

0

She evaluates none of them and gets the maximum value 0. Empty sequence is the shorter and lexicographically smaller than any other sequences.

Sample Input 4

5
-1 2 1 -2 -1

Sample Output for Input 4

3
1
2
4

She evaluates $\langle$ 1, 2, 4 $\rangle$ ones and gets the maximum value 4. Note that $\langle$ 2, 4, 5 $\rangle$ is not lexicographically smallest one.