Score : $200$ points

Problem Statement

There are non-negative integers $A$, $B$, $C$, $D$, $E$, and $F$, which satisfy $A\times B\times C\geq D\times E\times F$. Find the remainder when $(A\times B\times C)-(D\times E\times F)$ is divided by $998244353$.

Constraints

• $0\leq A,B,C,D,E,F\leq 10^{18}$
• $A\times B\times C\geq D\times E\times F$
• $A$, $B$, $C$, $D$, $E$, and $F$ are integers.

Input

The input is given from Standard Input in the following format:

$A$ $B$ $C$ $D$ $E$ $F$

Output

Print the remainder when $(A\times B\times C)-(D\times E\times F)$ is divided by $998244353$, as an integer.

2 3 5 1 2 4

22

Since $A\times B\times C=2\times 3\times 5=30$ and $D\times E\times F=1\times 2\times 4=8$, we have $(A\times B\times C)-(D\times E\times F)=22$. Divide this by $998244353$ and print the remainder, which is $22$.

1 1 1000000000 0 0 0

1755647

Since $A\times B\times C=1000000000$ and $D\times E\times F=0$, we have $(A\times B\times C)-(D\times E\times F)=1000000000$. Divide this by $998244353$ and print the remainder, which is $1755647$.

1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000

0

We have $(A\times B\times C)-(D\times E\times F)=0$. Divide this by $998244353$ and print the remainder, which is $0$.