Scientists have built a massive bacterial incubator. This incubator is a large rectangular parallelepiped with dimensions $n, m, k$, divided into $n \times m \times k$ small cells of size $1 \times 1 \times 1$. We establish a three-dimensional Cartesian coordinate system, using $(x, y, z)$ ($1 \leq x \leq n, 1 \leq y \leq m, 1 \leq z \leq k$) to describe the position of a small cell.

At the beginning of the experiment, each cell contains exactly $1$ bacterium. Every day thereafter, all bacteria divide. Suppose a bacterium at $(x, y, z)$ divides; it produces $6$ new bacteria, which move to the cells at $(x+1, y, z), (x-1, y, z), (x, y+1, z), (x, y-1, z), (x, y, z+1), (x, y, z-1)$. The original bacterium dies. Specifically, if a cell that a bacterium moves to does not exist, that bacterium dies instantly.

The experiment lasts for $d$ consecutive days. After $d$ days, the scientists want to know: how many bacteria are in the cell at $(a, b, c)$? Since the answer may be very large, you only need to output the value modulo $998244353$.

Input

A single line containing seven positive integers $d, n, m, k, a, b, c$.

Output

A single integer representing the answer modulo $998244353$.

Examples

Input 1

2 2 2 3 1 1 1

Output 1

10

Note 1

After the first day, it can be determined that all cells with $z=2$ have exactly $4$ bacteria, and all other cells have exactly $3$ bacteria. After the second day, the number of bacteria in cell $(1, 1, 1)$ is equal to the sum of the bacteria in cells $(1, 1, 2), (1, 2, 1), (2, 1, 1)$ at the end of the first day, which is $10$.

Input 2

2 2 2 3 1 1 2

Output 2

14

Input 3

50 49 44 48 49 15 25

Output 3

544847893

Input 4

120000 49997 49997 49993 46278 44140 26931

Output 4

139550295

Constraints

For all data, $1 \leq d, n, m, k \leq 1.2 \times 10^5, 1 \leq a \leq n, 1 \leq b \leq m, 1 \leq c \leq k$.

This problem consists of several subtasks. You must pass all test cases in a subtask to receive the points for that subtask.

• Subtask 1 ($5$ points): $d, n, m, k \leq 50$.
• Subtask 2 ($10$ points): $d, n, m, k \leq 5 \times 10^3$. Depends on Subtask 1.
• Subtask 3 ($15$ points): $m = k = 1$.
• Subtask 4 ($10$ points): $k = 1, n, m \geq d$.
• Subtask 5 ($15$ points): $k = 1, n, m \geq \frac{d}{10}$. Depends on Subtask 4.
• Subtask 6 ($35$ points): $k = 1$. Depends on Subtasks 3, 4, and 5.
• Subtask 7 ($10$ points): No special restrictions. Depends on Subtasks 1, 2, 3, 4, 5, and 6.