Farmer John Actually Farms

Farmer John is growing $N$ ($1 \leq N \leq 2\cdot 10^5$) asparagus plants on his farm. Some plants have genetic differences, so some grow faster than others. The initial height of the $i$th plant is $h_i$ inches, and each day the $i$th plant grows by $a_i$ inches.

FJ likes some of his plants more than others, so he wants certain plants to be taller than others. He gives you an array of distinct values $t_1,\dots,t_N$ that contains every integer from $0$ to $N-1$. He wants the $i$th plant to have exactly $t_i$ other plants that are taller than it. Find the minimum number of days needed to satisfy his request, or determine that it is impossible.

The first line contains an integer $T$ ($1 \leq T \leq 10$), the number of test cases.

Each test case starts with a line containing an integer $N$.

The second line contains $N$ integers $h_i$ ($1 \leq h_i \leq 10^9$), the initial height of the $i$th plant in inches.

The third line contains $N$ integers $a_i$ ($1 \leq a_i \leq 10^9$), the number of inches the $i$th plant grows each day.

The fourth line contains $N$ distinct integers $t_i$.

The sum of $N$ over all test cases does not exceed $2\cdot 10^5$.

Output $T$ lines, one per test case, each containing the answer. Output $-1$ if the request is impossible.

The values can be large, so use a 64-bit integer type such as long long in C/C++.