Problem Statement

There are $N$ types of stones, $1,2,\dots,N$. Stones of the same type all have the same weight. Takahashi and Aoki have $A_i$ and $B_i$ stones of type $i$, respectively. Determine whether there exists a sequence of positive integers $W=(W_1,W_2,\dots,W_N)$ satisfying the following conditions, and if it exists, construct one such sequence.

• $1 \leq W_i \leq 10^{18}$
• If the weight of a type-$i$ stone is $W_i$, the total weight of the stones Takahashi has is strictly greater than the total weight of the stones Aoki has.

Constraints

• $1 \leq N \leq 10^5$
• $1 \leq A_i \leq 10^9$
• $1 \leq B_i \leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

• $N$
• $A_1$ $A_2$ $\dots$ $A_N$
• $B_1$ $B_2$ $\dots$ $B_N$

Output

If there exists $W=(W_1,W_2,\dots,W_N)$ satisfying the conditions, output it in the following format:

• Yes
• $W_1$ $W_2$ $\dots$ $W_N$

If there is no $W=(W_1,W_2,\dots,W_N)$ satisfying the conditions, output No in one line.

3
4 7 4
5 5 5

Yes
4 7 4

If $W=(4,7,4)$, the total weight of the stones Takahashi has is $4 \times 4 + 7 \times 7 + 4 \times 4=81$. The total weight of the stones Aoki has is $4 \times 5 + 7 \times 5 + 4 \times 5=75$.

3
3 3 3
4 7 4

No

1
2
2

No

• Source: AtCoder ABC 474 D