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.

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.

Constraints

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

Sample Input 1

3
1 2 3
5 2 2

Sample Output 1

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}.

Sample Input 2

5
3 1 4 1 5
2 7 1 8 2

Sample Output 2

No

Sample Input 3

5
2 7 1 8 2
3 1 4 1 5

Sample Output 3

No

见题面 Input 部分

见题面 Output 部分