Problem Statement

You are given two integer sequences of length $N$: $A=(A_1,A_2,\dots,A_N)$ and $B=(B_1,B_2,\dots,B_N)$.

You may perform at most $31000$ operations of the following kind:

• Choose a pair of integers $(i,j)$ with $1 \le i < j \le N$, then replace $A_i$ with $A_j - 1$ and $A_j$ with $A_i + 1$.

Your goal is to make $A = B$. Determine whether the goal is achievable, and if it is, output one sequence of operations that achieves it.

Constraints

• $2 \le N \le 100$
• $1 \le A_i,B_i \le 100$

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 it is possible to make $A = B$, output Yes; otherwise, output No.

If you output Yes, also output an operation sequence in the following format:

M
i_1\ j_1
i_2\ j_2
\vdots
i_M\ j_M

$M$ is the length of the operation sequence and must satisfy $0 \le M \le 31000$. $i_k, j_k$ are the indices $i, j$ chosen in the $k$-th operation and must satisfy $1 \le i_k < j_k \le N$.

If multiple solutions exist, any of them will be accepted.