Problem Statement

There are three traffic lights numbered 1, 2, 3.
Traffic Light i eternally repeats the following pattern: green for g_i seconds, red for r_i seconds, green for g_i seconds, red for r_i seconds, and so on.
All three lights have turned green just now.
During the next (g_1 + r_1)(g_2 + r_2)(g_3 + r_3) seconds, what is the total duration of the time when all lights are green?
Compute the answer modulo 998,244,353.

Input

Input is given from Standard Input in the following format:
g_1 r_1 g_2 r_2 g_3 r_3

Output

Print the answer.

Constraints

• $1 \leq g_1, r_1, g_2, r_2, g_3, r_3 \leq 10^{12}$
• All values in the input are integers.

Sample Input 1

1 1 2 1 3 1

Sample Output 1

8

During the next 24 seconds,

• Light 1 is green during time intervals [0, 1], [2, 3], [4, 5], [6, 7], [8, 9], [10, 11], [12, 13], [14, 15], [16, 17], [18, 19], [20, 21], [22, 23].
• Light 2 is green during time intervals [0, 2], [3, 5], [6, 8], [9, 11], [12, 14], [15, 17], [18, 20], [21, 23].
• Light 3 is green during time intervals [0, 3], [4, 7], [8, 11], [12, 15], [16, 19], [20, 23].

Thus, all lights are green during time intervals [0, 1], [4, 5], [6, 7], [10, 11], [12, 13], [16, 17], [18, 19], [22, 23].
The total duration is 8 seconds.

Sample Input 2

7 3 5 7 11 4

Sample Output 2

420

Sample Input 3

999999999991 999999999992 999999999993 999999999994 999999999995 999999999996

Sample Output 3

120938286

见题面 Input 部分

见题面 Output 部分