| There are **K** families living in Christmasville. During Christmas they have | |
| this tradition, where each person secretly gets a gift for some other person. | |
| The assignment of who gives gift to whom is generally done by a lottery, but | |
| this time we are writing a program to do it. | |
| The assignment should have the following properties: | |
| * Each person should give exactly one gift. | |
| * Each person should receive exactly one gift. | |
| * A person should not give a gift to someone within the same family. | |
| Find out how many possible assignments are there, that satisfy above | |
| constraints. Two assignments are considered different, if there exists some | |
| person, who gives gifts to different people in the two assignments. Since this | |
| number may be very large, output this number modulo **1,000,000,007** | |
| ### Input | |
| The first line of the input consists of a single integer **T**, the number of | |
| test cases. | |
| Each test case starts with a line containing the integer **K**, the number of | |
| families. | |
| The next line of each test case contains **K** integers, **n1**, **n2**, ..., | |
| **nK**, where **ni** is the number of people in the **i**th family. | |
| ### Output | |
| For each test case **i** numbered from 1 to **T**, output "Case #**i**: ", | |
| followed by the number of valid assignments, modulo 1,000,000,007 | |
| ### Constraints | |
| 1 ≤ ** T ** ≤ 20 | |
| 2 ≤ ** K ** ≤ 100 | |
| 1 ≤ **ni** ≤ 4 | |
| 1 ≤ **n1** \+ **n2** \+ ... + **nK** ≤ 100 | |