Selecting Numbers

Problem Description

Given $n$ positive integers $a_1, a_2, \dots, a_n$. Choose some of them such that the sum of the chosen numbers satisfies $\bmod\ n = 0$ (each index may be chosen at most once).

Input Format

The first line contains an integer $n$, the number of values.

The next line contains $n$ integers $a_1, a_2, \dots, a_n$.

Output Format

On the first line, output $M$, the number of chosen numbers.

On the second line, output $M$ positive integers separated by spaces — the indices of the chosen numbers.

If there are multiple valid solutions, output any one of them.

If no valid solution exists, output $-1$.

Sample Input

4
1 3 2 5

Sample Output

2
2 4

Sample Explanation

$3 + 5 = 8$, and $8 \bmod 4 = 0$.

Constraints

All data satisfy $1 \le n \le 100000$ and $1 \le a_i \le 10^9$.