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 $0$s and $1$s 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 $A_{s + 3} = l$.

Constraints

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

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.