For two nonnegative integers $a, b$, let $a \wedge b$ be their bitwise AND, and $a \vee b$ be their bitwise OR.

You are given an array $A_0, A_1, \ldots, A_{2^N - 1}$ of length $2^N$ consisting of nonnegative integers. Please find a pair of indices $0 \le i, j \le 2^N - 1$ such that $A_{i} + A_{j} < A_{i \wedge j} + A_{i \vee j}$, or state that no such pair exists. If there is more than one such pair, find any one of them.

Input

The first line contains an integer $N$ ($0 \leq N \leq 20$).

The second line contains $2^N$ integers: $A_0, A_1, \ldots, A_{2^N - 1}$ ($0 \leq A_i \leq 10^7$).

Output

If there is an answer, output two integers $i$ and $j$ denoting the answer. The numbers $i$ and $j$ should be in the range $[0, 2^N - 1]$. Otherwise, output -1.

Examples

Input 1

2
0 1 1 2

Output 1

-1

Input 2

2
0 1 1 3

Output 2

2 1

Input 3

0
100

Output 3

-1