N. Ons Jabeur and the Perfect Consistency
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Ons Jabeur, the "Minister of Happiness" is training in Tunis for her next Grand Slam tournament. She believes that consistency is the key to winning the trophy.

Her coach has lined up N tennis balls, indexed from $$$1$$$ to $$$N$$$. The initial bounce rating of the $$$i-th$$$ ball is $$$A_i$$$ Ons wants to modify the ratings so that all balls eventually have the same value to ensure her practice is perfectly consistent. To modify the bounce ratings, she can perform a special technique. In one operation, she does the following:

  1. She calculates the smallest non-negative integer that does not currently appear in the array of bounce ratings.
  2. She chooses one ball at index $$$i$$$ ($$$1 \le i \le N$$$) and changes its bounce rating to that calculated value.

Help Ons determine if it is possible to make all bounce ratings equal. If it is possible, find the minimum number of operations $$$k$$$ and the sequence of indices $$$i_1, i_2, \dots, i_k$$$ to perform the operations.

If it is impossible to make all elements equal, output $$$-1$$$.

Input

The first line contains a single integer $$$N$$$ ($$$1 \le N \le 10^5$$$) — the number of tennis balls.

The second line contains $$$N$$$ integers $$$A_1, A_2, \dots, A_N$$$ ($$$0 \le A_i \le 10^9$$$) — the initial bounce ratings of the balls.

Output

If it is impossible to make all elements equal, print $$$-1$$$.

Otherwise, print the minimum number of operations $$$k$$$ on the first line, and the indices ($$$1-based$$$) of the balls chosen in each operation on the second line.

Example
Input
1
0
Output
0
Note

non-negative means $$$\ge 0$$$