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.

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.

Constraints

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

Sample Input 1

4
7 2 4 5
3 3 5 0

Sample Output 1

Yes
2
3 5
3 6

One can make A equal B as follows.

• Initially, A = (7,2,4,5).
• The operation with (x,y) = (3,5) makes A = (0,0,2,3).
• The operation with (x,y) = (3,6) makes A = (3,3,5,0).

Sample Input 2

1
5
3

Sample Output 2

Yes
1
2 4

Sample Input 3

2
3 1
3 1

Sample Output 3

Yes
0

Sample Input 4

2
0 0
1 2

Sample Output 4

No

见题面 Input 部分

见题面 Output 部分