Problem Statement

You are given $16 non-negative integers X_{i, j, k, l} (i, j, k, l \in$ $\lbrace 0, 1 \rbrace)$ in ascending order of (i, j, k, l).
Let $N = \displaystyle \sum_{i=0}^1 \sum_{j=0}^1 \sum_{k=0}^1 \sum_{l=0}^1 X_{i,j,k,l}$.
Find the number, modulo 998244353, of sequences (A_1, A_2, ..., A_{N+3}) of length N + 3 consisting of 0s and 1s that satisfy the following condition.

• For every quadruple of integers $(i, j, k, l) (i, j, k, l \in$ $\lbrace 0, 1 \rbrace),$ there are exactly X_{i,j,k,l} integers s between 1 and N, inclusive, that satisfy:
• A_s = i, A_{s + 1} = j, A_{s + 2} = k, and A_{s + 3} = l.

Input

The input is given from Standard Input in the following format:
X_{0,0,0,0} X_{0,0,0,1} X_{0,0,1,0} X_{0,0,1,1} X_{0,1,0,0} X_{0,1,0,1} X_{0,1,1,0} X_{0,1,1,1} X_{1,0,0,0} X_{1,0,0,1} X_{1,0,1,0} X_{1,0,1,1} X_{1,1,0,0} X_{1,1,0,1} X_{1,1,1,0} X_{1,1,1,1}

Output

Print the number, modulo 998244353, of sequences that satisfy the condition in the problem statement.

Constraints

• X_{i, j, k, l} are all non-negative integers.
• $1 \leq \displaystyle \sum_{i=0}^1 \sum_{j=0}^1 \sum_{k=0}^1 \sum_{l=0}^1 X_{i,j,k,l} \leq 10^6$

Sample Input 1

0 0 0 0 0 0 0 0 0 0 1 0 0 1 0 0

Sample Output 1

1

This input corresponds to the case where X_{1, 0, 1, 0} and X_{1, 1, 0, 1} are 1 and all others are 0.
In this case, only one sequence satisfies the condition, which is (1, 1, 0, 1, 0).

Sample Input 2

1 1 2 0 1 2 1 1 1 1 1 2 1 0 1 0

Sample Output 2

16

Sample Input 3

21 3 3 0 3 0 0 0 4 0 0 0 0 0 0 0

Sample Output 3

2024

Sample Input 4

62 67 59 58 58 69 57 66 67 50 68 65 59 64 67 61

Sample Output 4

741536606

见题面 Input 部分

见题面 Output 部分