F. Franklin is Back
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

Franklin Richards is a very curious and playful boy who, unlike other children, has extraordinary powers. Franklin has been watching YouTube videos about setting up domino tiles and how they fall one after the other. Inspired, Franklin decided to do something similar and created a bag from which he can draw any number of one-dimensional domino tiles of any height with infinitesimal width. He also created a one-dimensional play table.

Franklin drew $$$n$$$ domino tiles numbered from $$$1$$$ to $$$n$$$ and placed them vertically on the table (it seems impossible for them to balance, but since Franklin has powers beyond your imagination, this is possible). It is known that there is always an integer distance $$$x_i$$$ greater than $$$0$$$ between tile $$$i$$$ and tile $$$i - 1$$$, for each $$$i \gt 1$$$. After setting up all the tiles, Franklin thought that if he pushed one tile, it would trigger all the tiles to fall. Determine if Franklin is right. It is known that a domino tile $$$a$$$ can knock down another tile $$$b$$$ if the height $$$h_a$$$ is greater than the distance between $$$a$$$ and $$$b$$$ and tile $$$a$$$ falls towards $$$b$$$.

Input

The input consists of multiple test cases. The first line contains an integer $$$t$$$ $$$(1 \le t \le 10^4)$$$, the number of test cases. Each test case is described as follows:

First line: An integer $$$n$$$ $$$(2 \le n \le 10^5)$$$, the number of domino tiles.

Second line: $$$n$$$ integers $$$h_1, h_2, \ldots, h_n$$$ $$$(1 \le h_i \le 10^9)$$$, where $$$h_i$$$ represents the height of tile $$$i$$$.

Third line: $$$(n-1)$$$ integers $$$x_2, x_3, \ldots, x_n$$$ $$$(1 \le x_i \le 10^9)$$$, where $$$x_i$$$ is the distance between tile $$$i$$$ and tile $$$i-1$$$.

The sum of $$$n$$$ in all test cases does not exceed $$$10^5$$$.

Output

For each test case, print the word "habibi" if pushing any tile can cause all the others to fall, or "which" if it is not possible.

Example
Input
4
2
10 10
10
3
10 20 30
9 10
3
30 5 10
10 10
3
10 5 30
10 10
Output
which
habibi
habibi
habibi