Score : $1800$ points

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.

2 2 2 2

10

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

1 2 3 4

0

470000 480000 490000 500000

712808431