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 $998,244,353$.

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.

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.

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