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.

Sample Input 1

2 3 5 1 2 4

Sample Output 1

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~ .

Sample Input 2

1 1 1000000000 0 0 0

Sample Output 2

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~ .

Sample Input 3

1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000 1000000000000000000

Sample Output 3

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~ .