| 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.** |
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| ## Input |
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| 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. |
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| 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. |
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| ## Output |
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| 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**. |
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