We have a sequence of $N$ integers between $0$ and $9$ (inclusive): $A=(A_1, \dots, A_N)$, arranged from left to right in this order. Until the length of the sequence becomes $1$, we will repeatedly do the operation $F$ or $G$ below. - Operation $F$: delete the leftmost two values (let us call them $x$ and $y$) and then insert $(x+y)\%10$ to the left end. - Operation $G$: delete the leftmost two values (let us call them $x$ and $y$) and then insert $(x\times y)\%10$ to the left end. Here, $a\%b$ denotes the remainder when $a$ is divided by $b$. For each $K=0,1,\dots,9$, answer the following question. > Among the $2^{N-1}$ possible ways in which we do the operations, how many end up with $K$ being the final value of the sequence? > Since the answer can be enormous, find it modulo $998244353$.

Input is given from Standard Input in the following format: > $N$ > $A_1$ $\dots$ $A_N$ #### Constraints - $2 \leq N \leq 10^5$ - $0 \leq A_i \leq 9$ - All values in input are integers.

Print ten lines. The $i$\-th line should contain the answer for the case $K=i-1$.

AtCoder [ABC220D]