There are n bamboos of different weights W_i. There are n pandas of different capacity CAP_i. How many ways the pandas can carry the bamboos so that each panda carries exactly one bamboo, every bamboo is carried by one panda and a panda cannot carry a bamboo that is heavier than its capacity. Two ways will be considered different if at least one panda carries a different bamboo.

Input starts with an integer T (≤ 100), denoting the number of test cases.

Each case starts with a line containing an integer n (1 ≤ n ≤ 1000) denoting the number of pandas and bamboos. The next line contains n space separated distinct integers denoting the weights of be bamboos. The next line contains n space separated distinct integers denoting the capacities for the pandas. The weights and the capacities lie in the range [1, 10⁹].

For each case, print the case number and the number of ways those pandas can carry the bamboos. This number can be very big. So print the result modulo 1000 000 007.