Define the function ~f(i, j, k)~ recursively as follows:

Function f(i, j, k):
    if i = 0 and j = 0 and k = 0:
        return 1
    ans <- 0
    for x = 0 to i:
        for y = 0 to j:
            for z = 0 to k:
                if x = i and y = j and z = k:
                    continue
                ans <- ans + f(i-x, j-y, k-z) + f(x, y, z)
    return ans mod 998244353

You are given ~Q~ queries. Each query contains three non-negative integers ~i~, ~j~, and ~k~.

For each query, compute and output the value of ~f(i, j, k)~ modulo ~998244353~.

Input

The first line contains an integer ~Q~ — the number of queries.

Each of the next ~Q~ lines contains three integers ~i~, ~j~, and ~k~ describing one query.

Output

For each query, print one integer — the value of ~f(i, j, k)~ modulo ~998244353~.

Constraints

• ~1 \le Q \le 100~
• ~0 \le i, j, k \le 10^{5}~

Sample Input

3
1 2 3
4 5 6
7 8 9

Sample Output

7209
939856628
210934339