You are given an array $A$ consisting of $N$ integers. Your task is to find the longest subsequence S, such that XOR of any two elements in $S$ is non-zero.

You are required to print the size of $S (L)$ and the array of indices that are chosen for $S$. In case of multiple such arrays, choose the lexicographically smallest array.

Example: Let array A be [7, 9, 7], the maximum length of subsequence can be 2. There are two ways to choose a subsequence, [7, 9] and [9, 7]. The indices selected in the first case are [1, 2] while in the second they are [2, 3] so we need to choose [1, 2] as it is minimal.

Input format

• The first line contains an integer $T$ denoting the number of test cases.
• The first line of each test case contains an integer $N$ denoting the number of elements in array $A$.
• The second line of each test case contains $N$ space-separated integers of array $A$.

Output format

For each test case:

• The first line must contain the maximum size ($L$) of $S$ that can be chosen as a subsequence.
• The second line must contain space-separated integers denoting the lexicographically minimal array of indices that can be chosen.

Constraints

• $1 \leq T \leq 20000$
• $1 \leq N \leq 200000$
• $1 \leq A_i \leq 10^9$
• Sum of $N$ over all test cases will not exceed 200000.