MOD = 998244353

# Precompute ways for H=2, W>=3 case
ways = [0] * (18 + 1)
for c in range(19):
    if c <= 9:
        ways[c] = c + 1
    else:
        ways[c] = 19 - c

def compute_case(W, H, X):
    if H == 1 and W == 1:
        return 1 if 0 <= X <= 9 else 0
    elif (H == 1 and W == 2) or (W == 1 and H == 2):
        if X < 0 or X > 18:
            return 0
        if X <= 9:
            return (X + 1) % MOD
        else:
            return (19 - X) % MOD
    elif (H == 1 and W >= 3) or (W == 1 and H >= 3):
        return 1 if 0 <= X <= 9 else 0
    elif H == 2 and W == 2:
        def comb(n):
            if n < 0:
                return 0
            return n * (n-1) * (n-2) // 6 if n >= 3 else 0
        total = comb(X + 3)
        total -= 4 * comb(X + 3 - 10)
        total += 6 * comb(X + 3 - 20)
        total -= 4 * comb(X + 3 - 30)
        total += comb(X + 3 - 40)
        return total % MOD
    elif H == 2 or W == 2:
        if H != 2:
            W, H = H, W
        if H != 2:
            return 0
        if X < 0 or X > 36:
            return 0
        res = 0
        start = max(0, X - 18)
        end = min(18, X)
        for C1 in range(start, end + 1):
            C2 = X - C1
            if C2 < 0 or C2 > 18:
                continue
            res = (res + (ways[C1] ** 2) * (ways[C2] ** 2)) % MOD
        return res
    else:
        return 1 if X == 0 else 0

T = int(input())
for _ in range(T):
    W, H, X = map(int, input().split())
    result = compute_case(W, H, X)
    print(result % MOD)