Let's define the sum of two permutations *p* and *q* of numbers 0, 1, ..., (*n* - 1) as permutation <img align="middle" class="tex-formula" src="https://espresso.codeforces.com/a6967136eb87d05a01f795f6061b884a1a9f4f4b.png" style="max-width: 100.0%;max-height: 100.0%;"/>, where *Perm*(*x*) is the *x*-th lexicographically permutation of numbers 0, 1, ..., (*n* - 1) (counting from zero), and *Ord*(*p*) is the number of permutation *p* in the lexicographical order.

For example, *Perm*(0) = (0, 1, ..., *n* - 2, *n* - 1), *Perm*(*n*! - 1) = (*n* - 1, *n* - 2, ..., 1, 0)

Misha has two permutations, *p* and *q*. Your task is to find their sum.

Permutation *a* = (*a*<sub class="lower-index">0</sub>, *a*<sub class="lower-index">1</sub>, ..., *a*<sub class="lower-index">*n* - 1</sub>) is called to be lexicographically smaller than permutation *b* = (*b*<sub class="lower-index">0</sub>, *b*<sub class="lower-index">1</sub>, ..., *b*<sub class="lower-index">*n* - 1</sub>), if for some *k* following conditions hold: *a*<sub class="lower-index">0</sub> = *b*<sub class="lower-index">0</sub>, *a*<sub class="lower-index">1</sub> = *b*<sub class="lower-index">1</sub>, ..., *a*<sub class="lower-index">*k* - 1</sub> = *b*<sub class="lower-index">*k* - 1</sub>, *a*<sub class="lower-index">*k*</sub> &lt; *b*<sub class="lower-index">*k*</sub>.
The first line contains an integer *n* (1 ≤ *n* ≤ 200 000).

The second line contains *n* distinct integers from 0 to *n* - 1, separated by a space, forming permutation *p*.

The third line contains *n* distinct integers from 0 to *n* - 1, separated by spaces, forming permutation *q*.
print("_RANDOM_GUESS_1691656195.5377789")# 1691656195.5377913