Problem Statement

You are given sequences of non-negative integers: $A = (A_1, \ldots, A_N)$ and $B=(B_1, \ldots, B_N)$.

Determine whether one can make $A$ equal $B$ by performing the following operation between $0$ and $N$ times, inclusive.

• Operation: Choose integers $x,y$ such that $0\leq x < y\leq 10^{18}$. For every $i$, replace $A_i$ with $(A_i+x)\bmod y$.

If one can make $A$ equal $B$, print one way to do so.

Constraints

• $1\leq N\leq 1000$
• $0\leq A_i\leq 10^9$
• $0\leq B_i\leq 10^9$

Input

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

N
A_1 \ldots A_N
B_1 \ldots B_N

Output

If one cannot make $A$ equal $B$ by performing the operation between $0$ and $N$ times, inclusive, print No.

No

If one can do so, print one way in the following format:

Yes
K
x_1 y_1
\vdots
x_K y_K

Here, $K$ is the number of operations, and $x_i, y_i$ are integers $x, y$ chosen in the $i$-th operation. These must satisfy the following:

• $0\leq K\leq N$
• $0\leq x_i < y_i \leq 10^{18}$

If there are multiple ways to achieve the objective, you may print any of them.