Problem Statement

In the following undirected graph, count the number of walks from $S$ to $S$ that pass through the edges $ST$, $TU$, $UV$, $VS$ (in any direction) exactly $a$, $b$, $c$, $d$ times, respectively, modulo $998,244,353$.

Notes

A walk from $S$ to $S$ is a sequence of vertices $v_0 = S, v_1, \\ldots, v_k = S$ such that for each $i (0 \\leq i < k)$, there is an edge between $v_i$ and $v_{i+1}$. Two walks are considered distinct if they are distinct as sequences.

Constraints

• $1 \\leq a, b, c, d \\leq 500,000$
• All values in the input are integers.

Input

Input is given from Standard Input in the following format:

$a$ $b$ $c$ $d$

Output

Print the answer.

Sample Input 1

2 2 2 2

Sample Output 1

10

There are $10$ walks that satisfy the condition. One example of such a walk is $S$ $\\rightarrow$ $T$ $\\rightarrow$ $U$ $\\rightarrow$ $V$ $\\rightarrow$ $U$ $\\rightarrow$ $T$ $\\rightarrow$ $S$ $\\rightarrow$ $V$ $\\rightarrow$ $S$.

Sample Input 2

1 2 3 4

Sample Output 2

0

Sample Input 3

470000 480000 490000 500000

Sample Output 3

712808431