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:
where |s| is the length of the s.
N a_1 a_2 $\cdots$ a_N
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).
4 2 0 -2 1
1 1
She evaluates the first one and gets the maximum value 2.
3 2 -2 -2
3 1 2 3
She evaluates all of them and gets the maximum value 8.
2 -1 0
0
She evaluates none of them and gets the maximum value 0. Empty sequence is the shorter and lexicographically smaller than any other sequences.
5 -1 2 1 -2 -1
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.