write a go solution for Description:
Alice's potion making professor gave the following assignment to his students: brew a potion using n ingredients, such that the proportion of ingredient i in the final potion is r_i>0 (and r_1+r_2+*s+r_n=1).

He forgot the recipe, and now all he remembers is a set of n-1 facts of the form, "ingredients i and j should have a ratio of x to y" (i.e., if a_i and a_j are the amounts of ingredient i and j in the potion respectively, then it must hold a_i/a_j=x/y), where x and y are positive integers. However, it is guaranteed that the set of facts he remembers is sufficient to uniquely determine the original values r_i.

He decided that he will allow the students to pass the class as long as they submit a potion which satisfies all of the n-1 requirements (there may be many such satisfactory potions), and contains a positive integer amount of each ingredient.

Find the minimum total amount of ingredients needed to make a potion which passes the class. As the result can be very large, you should print the answer modulo 998,244,353.

Input Format:
The first line contains a single integer t (1<=t<=10^4) — the number of test cases.

The first line of each test case contains a single integer n (2<=n<=2*10^5).

Each of the next n-1 lines contains four integers i,j,x,y (1<=i,j<=n, inot=j, 1<=x,y<=n) — ingredients i and j should have a ratio of x to y. It is guaranteed that the set of facts is sufficient to uniquely determine the original values r_i.

It is also guaranteed that the sum of n for all test cases does not exceed 2*10^5.

Output Format:
For each test case, print the minimum total amount of ingredients needed to make a potion which passes the class, modulo 998,244,353.

Note:
In the first test case, the minimum total amount of ingredients is 69. In fact, the amounts of ingredients 1,2,3,4 of a valid potion are 16,12,9,32, respectively. The potion is valid because

- Ingredients 3 and 2 have a ratio of 9:12=3:4;
- Ingredients 1 and 2 have a ratio of 16:12=4:3;
- Ingredients 1 and 4 have a ratio of 16:32=2:4.

In the second test case, the amounts of ingredients 1,2,3,4,5,6,7,8 in the potion that minimizes the total amount of ingredients are 60,60,24,48,32,60,45,30.. Output only the code with no comments, explanation, or additional text.