Monocarp had an array $$$a$$$ consisting of $$$n$$$ integers. He has decided to choose two integers $$$l$$$ and $$$r$$$ such that $$$1 \le l \le r \le n$$$, and then sort the subarray $$$a[l..r]$$$ (the subarray $$$a[l..r]$$$ is the part of the array $$$a$$$ containing the elements $$$a_l, a_{l+1}, a_{l+2}, \dots, a_{r-1}, a_r$$$) in non-descending order. After sorting the subarray, Monocarp has obtained a new array, which we denote as $$$a'$$$.

For example, if $$$a = [6, 7, 3, 4, 4, 6, 5]$$$, and Monocarp has chosen $$$l = 2, r = 5$$$, then $$$a' = [6, 3, 4, 4, 7, 6, 5]$$$.

You are given the arrays $$$a$$$ and $$$a'$$$. Find the integers $$$l$$$ and $$$r$$$ that Monocarp could have chosen. If there are multiple pairs of values $$$(l, r)$$$, find the one which corresponds to the longest subarray.

Input

The first line contains one integer $$$t$$$ ($$$1 \le t \le 10^4$$$) — the number of test cases.

Each test case consists of three lines:

the first line contains one integer $$$n$$$ ($$$2 \le n \le 2 \cdot 10^5$$$);
the second line contains $$$n$$$ integers $$$a_1, a_2, \dots, a_n$$$ ($$$1 \le a_i \le n$$$);
the third line contains $$$n$$$ integers $$$a'_1, a'_2, \dots, a'_n$$$ ($$$1 \le a'_i \le n$$$).

Additional constraints on the input:

the sum of $$$n$$$ over all test cases does not exceed $$$2 \cdot 10^5$$$;
it is possible to obtain the array $$$a'$$$ by sorting one subarray of $$$a$$$;
$$$a' \ne a$$$ (there exists at least one position in which these two arrays are different).

Output

For each test case, print two integers — the values of $$$l$$$ and $$$r$$$ ($$$1 \le l \le r \le n$$$). If there are multiple answers, print the values that correspond to the longest subarray. If there are still multiple answers, print any of them.

Sort the Subarray

Examples