Problem Statement

Takahashi is in the square (0, 0, 0) in an infinite three-dimensional grid.
He can teleport between squares.
From the square (x, y, z), he can move to (x+1, y, z), (x-1, y, z), (x, y+1, z), (x, y-1, z), (x, y, z+1), or (x, y, z-1) in one teleport. (Note that he cannot stay in the square (x, y, z).)
Find the number of routes ending in the square (X, Y, Z) after exactly N teleports.
In other words, find the number of sequences of N+1 triples of integers $\big( (x_0, y_0, z_0), (x_1, y_1, z_1), (x_2, y_2, z_2), \ldots, (x_N, y_N, z_N)\big)$ that satisfy all three conditions below.

• (x_0, y_0, z_0) = (0, 0, 0).
• (x_N, y_N, z_N) = (X, Y, Z).
• |x_i-x_{i-1}| + |y_i-y_{i-1}| + |z_i-z_{i-1}| = 1 for each $i = 1, 2, \ldots, N$.

Since the number can be enormous, print it modulo 998244353.

Input

Input is given from Standard Input in the following format:
N X Y Z

Output

Print the number modulo 998244353.

Constraints

• $1 \leq N \leq 10^7$
• -$10^7 \leq X, Y, Z \leq 10^7$
• N, X, Y, and Z are integers.

Sample Input 1

3 2 0 -1

Sample Output 1

3

There are three routes ending in the square (2, 0, -1) after exactly 3 teleports:

• $(0, 0, 0) \rightarrow (1, 0, 0) \rightarrow (2, 0, 0) \rightarrow(2, 0, -1)$
• $(0, 0, 0) \rightarrow (1, 0, 0) \rightarrow (1, 0, -1) \rightarrow(2, 0, -1)$
• $(0, 0, 0) \rightarrow (0, 0, -1) \rightarrow (1, 0, -1) \rightarrow(2, 0, -1)$

Sample Input 2

1 0 0 0

Sample Output 2

0

Note that exactly N teleports should be performed, and they do not allow him to stay in the same position.

Sample Input 3

314 15 92 65

Sample Output 3

106580952

Be sure to print the number modulo 998244353.

见题面 Input 部分

见题面 Output 部分