https://www.acmicpc.net/problem/19594
"""
Title : 슈퍼컴퓨터
Link : https://www.acmicpc.net/problem/19594
"""
import sys
input = sys.stdin.readline
def solve(n, hours, deadlines):
dh_list = [(i, j) for i, j in zip(deadlines, hours)]
dh_list.sort(key=lambda x:x[0])
s = 0
late_list = []
for d, h in dh_list:
s += h
late_list.append(max(0, s-d))
i_max_late_list = []
temp_max_late = 0
for l in late_list:
temp_max_late = max(l, temp_max_late)
i_max_late_list.append(temp_max_late)
answer = max(i_max_late_list[-1] - (dh_list[0][1]-1), 0)
for i in range(1, n):
tmp = max(i_max_late_list[i-1], max(i_max_late_list[-1] - (dh_list[i][1]-1), 0))
answer = min(answer, tmp)
return answer
t = int(input())
for _ in range(t):
n = int(input())
h = list(map(int, input().split()))
d = list(map(int, input().split()))
print(solve(n, h, d))