Subarray with maximum XOR.

Very easy

Execution time limit is 1 second

Runtime memory usage limit is 256 megabytes

Given an array of integers. Find the subarray with maximum XOR.

Input

The first line contains the size of array $n (n \leq 1 0^{5})$ . Second line contains $n$ integers $a_{1}, a_{2}, ..., a_{n} (0 \leq a_{i} \leq 1 0^{18})$ .

Output

Print such $l$ and $r$ for which the value $a_{l} x or a_{l + 1} x or ... x or a_{r}$ is maximum among all possible subarrays $[l ... r] (1 \leq l \leq r \leq n)$ . Then in the same line print the value of maximum XOR.

Examples

Input #1

Answer #1

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