Score : $300$ points

Problem Statement

You are given two integer sequences of length $N$: $a_1,a_2,..,a_N$ and $b_1,b_2,..,b_N$. Determine if we can repeat the following operation zero or more times so that the sequences $a$ and $b$ become equal.

Operation: Choose two integers $i$ and $j$ (possibly the same) between $1$ and $N$ (inclusive), then perform the following two actions simultaneously:

• Add $2$ to $a_i$.
• Add $1$ to $b_j$.

Constraints

• $1 \leq N \leq 10$ $000$
• $0 \leq a_i,b_i \leq 10^9$ ($1 \leq i \leq N$)
• All input values are integers.

Input

Input is given from Standard Input in the following format:

$N$

$a_1$ $a_2$ $..$ $a_N$

$b_1$ $b_2$ $..$ $b_N$

Output

If we can repeat the operation zero or more times so that the sequences $a$ and $b$ become equal, print Yes; otherwise, print No.

3
1 2 3
5 2 2

Yes

For example, we can perform three operations as follows to do our job:

• First operation: $i=1$ and $j=2$. Now we have $a = \{3,2,3\}$, $b = \{5,3,2\}$.
• Second operation: $i=1$ and $j=2$. Now we have $a = \{5,2,3\}$, $b = \{5,4,2\}$.
• Third operation: $i=2$ and $j=3$. Now we have $a = \{5,4,3\}$, $b = \{5,4,3\}$.

5
3 1 4 1 5
2 7 1 8 2

No

5
2 7 1 8 2
3 1 4 1 5

No