B - Orthogonality

Score : $200$ points

Problem Statement

Given are two $N$-dimensional vectors $A = (A_1, A_2, A_3, \dots, A_N)$ and $B = (B_1, B_2, B_3, \dots, B_N)$.
Determine whether the inner product of $A$ and $B$ is $0$.
In other words, determine whether $A_1B_1 + A_2B_2 + A_3B_3 + \dots + A_NB_N = 0$.

Constraints

• $1 \le N \le 100000$
• $-100 \le A_i \le 100$
• $-100 \le B_i \le 100$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$A_1$ $A_2$ $A_3$ $\dots$ $A_N$

$B_1$ $B_2$ $B_3$ $\dots$ $B_N$

Output

If the inner product of $A$ and $B$ is $0$, print Yes; otherwise, print No.

2
-3 6
4 2

Yes

The inner product of $A$ and $B$ is $(-3) \times 4 + 6 \times 2 = 0$.

2
4 5
-1 -3

No

The inner product of $A$ and $B$ is $4 \times (-1) + 5 \times (-3) = -19$.

3
1 3 5
3 -6 3

Yes

The inner product of $A$ and $B$ is $1 \times 3 + 3 \times (-6) + 5 \times 3 = 0$.