| In this problem you need to count number of possible permutations **p** of the | |
| first **N** integers, given **N-1** constraints of the form **pi < pj.** | |
| ## Input | |
| The first line contains an integer **T**, **T** ≤ 20, followed by **T** test | |
| cases. Each test case begins with an integer **N**, **N** ≤ 1,000, which is | |
| the number of integers in the permutation. The next **N - 1** lines each | |
| contain a single constraint in the following format: "**i** **sign** **j**", | |
| where 0 ≤ **i**, **j** ≤ **N - 1** and **sign** is either "**<**" or "**>**", | |
| which denotes whether the **i**-th element of the permutation should be less | |
| than or greater than the **j**-th element. | |
| It is guaranteed that it is not possible to partition indices into two | |
| disjoint sets A and B such that there is no constraint involving elements from | |
| both A and B. | |
| ## Output | |
| For each test case, output one single line with the number of permutations | |
| that satisfy all the constraints, following the output format shown in the | |
| example. The answer may be very large, so you should give the result modulo | |
| **1,000,000,007**. | |